mat 540 complete course mat540 complete course
DESCRIPTION
MAT 540 Complete Course MAT540 Complete Course Click Link for the Answer: http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085MAT 540 Week 1 Discussion"Class Introductions" Please respond to the following:• Please introduce yourself, including your educational and career goals, as well as some personal information about yourself. In your introduction, please draw from your own experience (or use a search engine) to give an example of how probability is used in your chosen profession. If you get your information from an online or other resource, be sure to cite the source of the information.MAT 540 Week 1 HomeworkChapter 11. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is$65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit.b. Determine the annual break-even volume for the Retread Tire Company operation.2. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000,and its variable cost per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 perpound. Determine the monthly break-even volume for the company.3. If Evergreen Fertilizer Company in problem 2 changes the price of its fertilizer from $0.45 perpound to $0.55 per pound, what effect will the change have on the break-even volume?4. If Evergreen Fertilizer Company increases its advertising expenditure by $10,000 per year, whateffect will the increase have on the break-even volume computed in problem 2?5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadiumduring home games. There are 6 home games scheduled for the upcoming season. She must pay theTech athletic department a vendor’s fee of $3,000 for the season. Her stand and other equipmentwill cost her $3,500 for the season. She estimates that each hot dog she sells will cost her $0.40. shehas talked to friends at other universities who sell hot dogs at games. Based on their informationand the athletic department’s forecast that each game will sell out, she anticipates that she will sellapproximately 1,500 hot dogs during each game.a. What price should she charge for a hot dog in order to break even?b. What factors might occur during the season that would alter the volume sold and thus thebreak-even price Annie might charge?6. The college of business at Kerouac University is planning to begin an online MBA program. Theinitial start-up cost for computing equipment, facilities, course development and staff recruitmentand development is $400,000. The college plans to charge tuition of $20,000 per student per year.However, the university administration will charge the college $10,000 per student for the first 100students enrolled each year for administrative costs and its share of the tuition payments.a. How many students does the college need to enroll in the first year to break-even?b. If the college can enroll 80 students the first year, how much profit will it make?c. The college believes it can increase tuition to $25,000, but doing so would reduce enrollment to50. Should the college consider doing this?Chapter 117. The following probabilities for grades in management science have been determined based on pastrecords: The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine theexpected grade and variance for the course.8. An investment firm is considering two alternative investments, A and B, under two possible futuresets of economic conditions good and poor. There is a .60 probability of good economic conditionsoccurring and a .40 probability of poor economic conditions occurring. The expected gains andlosses unTRANSCRIPT
MAT 540 Complete Course MAT540 Complete Course
Click Link for the Answer:
http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085
http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085
MAT 540 Week 1 Discussion
"Class Introductions" Please respond to the following:
Please introduce yourself, including your educational and career goals, as well as some
personal information about yourself. In your introduction, please draw from your own
experience (or use a search engine) to give an example of how probability is used in your
chosen profession. If you get your information from an online or other resource, be sure to
cite the source of the information.
MAT 540 Week 1 Homework
Chapter 1
1. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is
$65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire Company operation.
2. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is
$25,000,
and its variable cost per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 per
pound. Determine the monthly break-even volume for the company.
3. If Evergreen Fertilizer Company in problem 2 changes the price of its fertilizer from $0.45 per
pound to $0.55 per pound, what effect will the change have on the break-even volume?
4. If Evergreen Fertilizer Company increases its advertising expenditure by $10,000 per year,
what
effect will the increase have on the break-even volume computed in problem 2?
5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium
during home games. There are 6 home games scheduled for the upcoming season. She must pay
the
Tech athletic department a vendor’s fee of $3,000 for the season. Her stand and other equipment
will cost her $3,500 for the season. She estimates that each hot dog she sells will cost her $0.40.
she
has talked to friends at other universities who sell hot dogs at games. Based on their information
and the athletic department’s forecast that each game will sell out, she anticipates that she will sell
approximately 1,500 hot dogs during each game.
a. What price should she charge for a hot dog in order to break even?
b. What factors might occur during the season that would alter the volume sold and thus the
break-even price Annie might charge?
6. The college of business at Kerouac University is planning to begin an online MBA program.
The
initial start-up cost for computing equipment, facilities, course development and staff recruitment
and development is $400,000. The college plans to charge tuition of $20,000 per student per year.
However, the university administration will charge the college $10,000 per student for the first
100
students enrolled each year for administrative costs and its share of the tuition payments.
a. How many students does the college need to enroll in the first year to break-even?
b. If the college can enroll 80 students the first year, how much profit will it make?
c. The college believes it can increase tuition to $25,000, but doing so would reduce enrollment to
50. Should the college consider doing this?
Chapter 11
7. The following probabilities for grades in management science have been determined based on
past
records:
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the
expected grade and variance for the course.
8. An investment firm is considering two alternative investments, A and B, under two possible
future
sets of economic conditions good and poor. There is a .60 probability of good economic
conditions
occurring and a .40 probability of poor economic conditions occurring. The expected gains and
losses under each economic type of conditions are shown in the following table:
Using the expected value of each investment alternative, determine which should be selected.
9. The weight of the bags of fertilizer is normally distributed, with a mean of 45 pounds and a
standard deviation of 5 pounds. What is the probability that a bag of fertilizer will weigh between
38 and 50 pounds?
10. The polo Development Firm is building a shopping center. It has informed renters that their
rental
spaces will be ready for occupancy in 18 months. If the expected time until the shopping center is
completed is estimated to be 15 months, with a standard deviation of 5 months, what is the
probability that the renters will not be able to occupy in 18 months?
11. The manager of the local National Video Store sells videocassette recorders at discount prices.
If
the store does not have a video recorder in stock when a customer wants to buy one, it will lose
the
sale because the customer will purchase a recorder from one of the many local competitors. The
problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet
all demand is excessively high. The manager has determined that if 85% of customer demand for
recorders can be met, then the combined cost of lost sales and inventory will be minimized. The
manager has estimated that monthly demand for recorders is normally distributed, with a mean of
175 recorders and a standard deviation of 55. Determine the number of recorders the manager
should order each month to meet 85% of customer demand.
MAT 540 Week 2 Discussion
In your own words, explain how to obtain the “expected value of perfect information” for any
payoff table, which has probabilities associated with each state of nature. Then, provide an
example, drawing from any of the payoff tables in Problems 1-17 in the back of Chapter 12. If no
probabilities are given for the states of nature, then assume equal likelihood.
MAT 540 Week 2 Homework
Chapter 12
1. A local real estate investor in Orlando is considering three alternative investments; a motel, a
restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of
gasoline and the number of tourists; profits from the theater will be relatively stable under any
conditions. The following payoff table shows the profit or loss that could result from each
investment:
Determine the best investment, using the following decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz (α = 0.4)
e. Equal likelihood
2. A concessions manager at the Tech versus A&M football game must decide whether to have
the
vendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast
skies,
and a 40% chance of sunshine, according to the weather forecast in college junction, where the
game is to be held. The manager estimates that the following profits will result from each
decision,
given each set of weather conditions:
a. Compute the expected value for each decision and select the best one.
b. Develop the opportunity loss table and compute the expected opportunity loss for each
decision.
3. Place-Plus, a real estate development firm, is considering several alternative development
projects.
These include building and leasing an office park, purchasing a parcel of land and building an
office building to rent, buying and leasing a warehouse, building a strip mall, and selling
condominiums. The financial success of these projects depends on interest rate movement in the
next 5 years. The various development projects and their 5- year financial return (in $1,000,000s)
given that interest rates will decline, remain stable, or increase, are in the following payoff table.
Place-Plus real estate development firm has hired an economist to assign a probability to each
direction interest rates may take over the next 5 years. The economist has determined that there is
a
0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and
a
0.2 probability that rates will increase.
a. Using expected value, determine the best project.
b. Determine the expected value of perfect information.
4. The
director
of career advising at Orange Community College wants to use decision analysis to
provide information to help students decide which 2-year degree program they should pursue. The
director has set up the following payoff table for six of the most popular and successful degree
programs at OCC that shows the estimated 5-Year gross income ($) from each degree for four
future economic conditions:
Determine the best degree program in terms of projected income, using the following decision
criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz (α=0.4)
5. Construct a decision tree for the following decision situation and indicate the best decision.
Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new
dealership.
They have three offers: from a foreign compact car company, from a U.S. producer of full-sized
cars, and from a truck company. The success of each type of dealership will depend on how much
gasoline is going to be available during the next few years. The profit from each type of
dealership,
given the availability of gas, is shown in the following payoff table:
Decision Tree diagram to complete:
MAT 540 Week 2 Quiz
Question 1
Probabilistic techniques assume that no uncertainty exists in model parameters.
Question 2
In general, an increase in price increases the break even point if all costs are held constant.
Question 3
Parameters are known, constant values that are usually coefficients of variables in equations.
Question 4
Fixed cost is the difference between total cost and total variable cost.
Question 5
P(A | B) is the probability of event A, if we already know that event B has occurred.
Question 6
A binomial probability distribution indicates the probability of r successes in n trials.
Question 7
If events A and B are independent, then P(A|B) = P(B|A).
Question 8
If fixed costs increase, but variable cost and price remain the same, the break even point
Question 9
If the price increases but fixed and variable costs do not change, the break even point
Question 10
A model is a functional relationship that includes:
Question 11
The indicator that results in total revenues being equal to total cost is called the
Question 12
The expected value of the standard normal distribution is equal to
Question 13
The area under the normal curve represents probability, and the total area under the curve sums to
Question 14
In a binomial distribution, for each of n trials, the event
Question 15
Administrators at a university are planning to offer a summer seminar. The costs of reserving a
room, hiring an instructor, and bringing in the equipment amount to $3000.
Suppose that it costs $25 per student for the administrators to provide the course materials. If we
know that 20 people will attend, what price should be charged per person to break even? Note:
please report the result as a whole number, rounding if necessary and omitting the decimal point.
Question 16
A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is
$3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be
chosen in order to break even at the end of the month? Note: please report the result as a whole
number, rounding if necessary and omitting the decimal point.
Question 17
A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the
revenue per unit is projected to be $45. Find the break-even point.
Question 18
Wei is considering pursuing an MS in Information Systems degree. She has applied to two
different universities. The acceptance rate for applicants with similar qualifications is 20% for
University X and 45% for University Y. What is the probability that Wei will be accepted by at
least one of the two universities? {Express your answer as a percent. Round (if necessary) to the
nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20}
Question 19
Employees of a local company are classified according to gender and job type. The following
table summarizes the number of people in each job category.
Question 20
An automotive center keeps tracks of customer complaints received each week. The probability
distribution for complaints can be represented as a table (shown below). The random variable xi
represents the number of complaints, and p(xi) is the probability of receiving xi complaints.
MAT 540 Week 3 Discussion
Discuss Simulation
Select one (1) of the following topics for your primary discussion posting:
Identify the part of setting up a simulation in Excel that you find to be the most
challenging, and explain why. Identify resources that can help you with that.
Explain how simulation is used in the real world. Provide a specific example from your
own line of work, or a line of work that you find particularly interesting.
MAT 540 Week 3 Homework
Chapter 14
1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according
to
the following probability distribution. The squad is on duty 24 hours per day, 7 days per week:
a. Simulate the emergency calls for 3 days (note that this will require a “running” , or
cumulative,hourly clock), using the random number table.
b. Compute the average time between calls and compare this value with the expected value
of the time between calls from the probability distribution. Why are the result different?
2. The time between arrivals of cars at the Petroco Services Station is defined by the following
probability distribution:
a. Simulate the arrival of cars at the service station for 20 arrivals and compute the average
time
between arrivals.
b. Simulate the arrival of cars at the service station for 1 hour, using a different stream of
random
numbers from those used in (a) and compute the average time between arrivals.
c. Compare the results obtained in (a) and (b).
3. The Dynaco Manufacturing Company produces a product in a process consisting of operations
of
five machines. The probability distribution of the number of machines that will break down in a
week follows
a. Simulate the machine breakdowns per week for 20 weeks.
b. Compute the average number of machines that will break down per week.
4. Simulate the following decision situation for 20 weeks, and recommend the best decision.
A concessions manager at the Tech versus A&M football game must decide whether to have the
vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast
skies,
and a 55% chance of sunshine, according to the weather forecast in college junction, where the
game is to be held. The manager estimates that the following profits will result from each
decision,
given each set of weather conditions:
5. Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either
1, 2,
or 3 hours are required to fix it, according to the following probability distribution:
Simulate the repair time for 20 weeks and then compute the average weekly repair time.
MAT 540 Week 3 Quiz 2
Question 1
If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)
Question 2
Probability trees are used only to compute conditional probabilities.
Question 3
Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is
normally distributed.
Question 4
Both maximin and minimin criteria are optimistic.
Question 5
The minimin criterion is optimistic.
Question 6
The Hurwicz criterion is a compromise between the maximax and maximin criteria.
Question 7
The Hurwicz criterion is a compromise between the minimax and minimin criteria.
Question 8
The chi-square test is a statistical test to see if an observed data fit a _________.
Question 9
Assume that it takes a college student an average of 5 minutes to find a parking spot in the main
parking lot. Assume also that this time is normally distributed with a standard deviation of 2
minutes. Find the probability that a randomly selected college student will take between 2 and 6
minutes to find a parking spot in the main parking lot.
Question 10
A professor would like to utilize the normal distribution to assign grades such that 5% of students
receive A's. If the exam average is 62 with a standard deviation of 13, what grade should be the
cutoff for an A? (Round your answer.)
Question 11
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
If the probability of brisk business is .40 and for slow business is .60, the expected value of
perfect information is:
Question 12
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
The maximin strategy is:
Question 13
The maximin criterion results in the
Question 14
Determining the worst payoff for each alternative and choosing the alternative with the best worst
is called
Question 15
A life insurance company wants to update its actuarial tables. Assume that the probability
distribution of the lifetimes of the participants is approximately a normal distribution with a mean
of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are
expected to see their 75th birthday? Note: Write your answers with two places after the decimal,
rounding off as appropriate.
Question 16
A brand of television has a lifetime that is normally distributed with a mean of 7 years and a
standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more
than 8 years? Note: Write your answers with two places after the decimal, rounding off as
appropriate.
Question 17
A manager has developed a payoff table that indicates the profits associated with a set of
alternatives under 2 possible states of nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
What is the highest expected value? Assume that the probability of S2 is equal to 0.4.
Question 18
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
If the probability of brisk business is .40, what is the numerical maximum expected value?
Question 19
A manager has developed a payoff table that indicates the profits associated with a set of
alternatives under 2 possible states of nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
Compute the expected value of perfect information assuming that the probability of S2 is equal to
0.4.
Question 20
A group of friends are planning a recreational outing and have constructed the following payoff
table to help them decide which activity to engage in. Assume that the payoffs represent their
level of enjoyment for each activity under the various weather conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4,
and 0.4, respectively what is the EVPI for this situation?
MAT 540 Week 4 Discussion
Discuss Forecasting Methods
Select one (1) of the following topics for your primary discussion posting:
Identify any challenges you have in setting up a time-series analysis in Excel. Explain
what they are and why they are challenging. Identify resources that can help you with that.
Explain how forecasting is used in the real world. Provide a specific example from your
own line of work, or a line of work that you find particularly interesting.
MAT 540 Week 4 Homework
Chapter 15
1. The manager of the Carpet City outlet needs to make an accurate forecast of the demand for
Soft
Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill,
customer will buy their carpet from one of Carpet City’s many competitors. The manager has
collected the following demand data for the past 8 months:
a. Compute a 3-month moving average forecast for months 4 through 9.
b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign
weights of 0.55, 0.35, and 0.10 to the months in sequence, starting with the most recent
month.
c. Compare the two forecasts by using MAD. Which forecast appears to be more accurate?
2. The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline
next month so that the proper number of gallons can be ordered from the distributor. The owner
has
accumulated the following data on demand for unleaded gasoline from sales during the past 10
months:
a. Compute an exponential smoothed forecast, using an α value of 0.4
b. Compute the MAD.
3. Emily Andrews has invested in a science and technology mutual fund. Now she is considering
liquidating and investing in another fund. She would like to forecast the price of the science and
technology fund for the next month before making a decision. She has collected the following data
on the average price of the fund during the past 20 months:
a. Using a 3-month average, forecast the fund price for month 21.
b. Using a 3-month weighted average with the most recent month weighted 0.5, the next
most
recent month weighted 0.30, and the third month weighted 0.20, forecast the fund price for
month 21.
c. Compute an exponentially smoothed forecast, using α=0.3, and forecast the fund price
for
month 21.
d. Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.
4. Carpet City wants to develop a means to forecast its carpet sales. The store manager believes
that
the store’s sales are directly related to the number of new housing starts in town. The manager has
gathered data from county records on monthly house construction permits and from store records
on monthly sales. These data are as follows:
a. Develop a linear regression model for these data and forecast carpet sales if 30
construction
permits for new homes are filed.
b. Determine the strength of the causal relationship between monthly sales and new home
construction by using correlation.
5. The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice
cream.
The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses
business, and if it orders too much, the extra must be thrown away. The manager belives that a
major determinant of ice cream sales is temperature (i.e.,the hotter the weather, the more ice
cream
people buy). Using an almanac, the manager has determined the average day time temperature for
14 weeks, selected at random, and from store records he has determined the ice cream
consumption
for the same 14 weeks. These data are summarized as follows:
a. Develop a linear regression model for these data and forecast the ice cream consumption if the
average weekly daytime temperature is expected to be 85 degrees.
b. Determine the strength of the linear relationship between temperature and ice cream
consumption by using correlation.
c. What is the coefficient of determination? Explain its meaning
MAT 540 Week 5 Discussion
"Reflection to date" Please respond to the following:
In a paragraph, reflect on what you've learned so far in this course. Identify the most
interesting, unexpected, or useful thing you've learned and explain why
MAT 540 Week 5 Midterm Exam
Question 1
Deterministic techniques assume that no uncertainty exists in model parameters.
Question 2
A continuous random variable may assume only integer values within a given interval.
Question 3
An inspector correctly identifies defective products 90% of the time. For the next 10 products, the
probability that he makes fewer than 2 incorrect inspections is 0.736.
Question 4
A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and
branches.
Question 5
A table of random numbers must be normally distributed and efficiently generated.
Question 6
Simulation results will always equal analytical results if 30 trials of the simulation have been
conducted.
Question 7
Data cannot exhibit both trend and cyclical patterns.
Question 8
Qualitative methods are the least common type of forecasting method for the long-term strategic
planning process.
A company markets educational software products, and is ready to place three new products on
the market. Past experience has shown that for this particular software, the chance of "success" is
80%. Assume that the probability of success is independent for each product. What is the
probability that exactly 1 of the 3 products is successful?
Assume that it takes a college student an average of 5 minutes to find a parking spot in the main
parking lot. Assume also that this time is normally distributed with a standard deviation of 2
minutes. What time is exceeded by approximately 75% of the college students when trying to find
a parking spot in the main parking lot?
Question 11
The __________ is the maximum amount a decision maker would pay for additional information.
Question 12
Random numbers generated by a __________ process instead of a __________ process are
pseudorandom numbers.
Question 13
Two hundred simulation runs were completed using the probability of a machine breakdown from
the table below. The average number of breakdowns from the simulation trials was 1.93 with a
standard deviation of 0.20.
No. of breakdowns per week
Probability
Cumulative probability
0
.10
.07
1.00
What is the probability of 2 or fewer breakdowns?
Question 14
A seed value is a(n)
Question 15
Pseudorandom numbers exhibit __________ in order to be considered truly random.
Question 16
Given the following data on the number of pints of ice cream sold at a local ice cream store for a
6-period time frame:
If the forecast for period 5 is equal to 275, use exponential smoothing with α = .40 to compute a
forecast for period 7.
Question 17
rob
14, and 15)estion worth 2 points, 1 hour time limit (chapters 1,ue units EXCEPT:The U.S.
Department of Agriculture estimates that the yearly yield of limes per acre is distributed as
follows:
Yield, bushels per acre
Probability
350
.10
400
.18
450
.50
500
.22
The estimated average price per bushel is $16.80.
What is the expected yield of the crop?
Question 18
__________ is a linear regression model relating demand to time.
Question 19
Coefficient of determination is the percentage of the variation in the __________ variable that
results from the __________ variable.
Question 20
Which of the following possible values of alpha would cause exponential smoothing to respond
the most slowly to sudden changes in forecast errors?
Question 21
__________ is a measure of the strength of the relationship between independent and dependent
variables.
Question 22
__________ is absolute error as a percentage of demand.
Correct Answer:
MAPD
Question 23
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Question 24
In exponential smoothing, the closer alpha is to __________, the greater the reaction to the most
recent demand.
Question 25
An online sweepstakes has the following payoffs and probabilities. Each person is limited to one
entry.
The probability of winning at least $1,000.00 is ________.
Question 26
An automotive center keeps tracks of customer complaints received each week. The probability
distribution for complaints can be represented as a table or a graph, both shown below. The
random variable xi represents the number of complaints, and p(xi) is the probability of receiving
xi complaints.
xi
0
1
2
3
4
5
6
p(xi)
.10
.15
.18
.20
.20
.10
.07
What is the average number of complaints received per week? Round your answer to two places
after the decimal.
Question 27
A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur
between 2 and 4 times? Round your answer to four places after the decimal.
Question 28
The drying rate in an industrial process is dependent on many factors and varies according to the
following distribution.
Compute the mean drying time. Use two places after the decimal.
Question 29
An investor is considering 4 different opportunities, A, B, C, or D. The payoff for each
opportunity will depend on the economic conditions, represented in the payoff table below.
Economic Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what is
the highest expected payoff?
Question 30
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary
workers. He estimates that net revenues will vary with how well taxpayers comply with the new
tax code. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).
If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%
respectively, what is the expected value of perfect information? Note: Please express your
answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest
whole number, if necessary.
Question 31
A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to
simulate one value from this distribution, and has drawn the number 1.4 randomly. What is the
simulated value?
Question 32
Robert wants to know if there is a relation between money spent on gambling and winnings.
What is the coefficient of determination? Note: please report your answer with 2 places after the
decimal point.
Question 33
Given the following data on the number of pints of ice cream sold at a local ice cream store for a
6-period time frame:
Compute a 3-period moving average for period 6. Use two places after the decimal.
Question 34
The following sales data are available for 2003-2008.
Determine a 4-year weighted moving average forecast for 2009, where weights are W1 = 0.1, W2
= 0.2, W3 = 0.2 and W4 = 0.5.
Question 35
The following data summarizes the historical demand for a product.
Month
Actual Demand
March
20
April
25
May
40
June
35
July
30
August
45
Use exponential smoothing with α = .2 and the smoothed forecast for July is 32. Determine the
smoothed forecast for August.
Question 36
The following data summarizes the historical demand for a product
Month
Actual Demand
March
20
April
If the forecasted demand for June, July and August is 32, 38 and 42, respectively, what is MAPD?
Write your answer in decimal form and not in percentages. For example, 15% should be written as
0.15. Use three significant digits after the decimal.
Question 37
Daily highs in Sacramento for the past week (from least to most recent) were: 95, 102, 101, 96,
95, 90 and 92. Develop a forecast for today using a 2 day moving average.
Question 38
Given the following data on the number of pints of ice cream sold at a local ice cream store for a
6-period time frame:
Compute a 3-period moving average for period 4. Use two places after the decimal.
Question 39
Given the following data, compute the MAD for the forecast.
Year Demand Forecast
2001
16
18
2002
20
19
2003
18
24
Question 40
Consider the following annual sales data for 2001-2008.
Year
Sales
2001
2
2002
4
20
Calculate the correlation coefficient . Use four significant digits after the decimal.
MAT 540 Week 6 Discussion
Discuss LP Models
Select one (1) of the following topics for your primary discussion posting:
The objective function always includes all of the decision variables, but that is not
necessarily true of the constraints. Explain the difference between the objective function
and the constraints. Then, explain why a constraint need not refer to all the variables.
Pick any constraint from any problem in the text, and explain how to plot the line that
corresponds to that constraint.
MAT 540 Week 6 Homework
Chapter 2
1. A Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats
and rice, provide vitamins A and B. The company wants to know how many ounces of oats
and rice it should include in each box of cereal to meet the minimum requirements of 45
milligrams of vitamin A and 13 milligrams of vitamin B while minimizing cost. An ounce
of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, whereas an
ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs
$0.06, and an ounce of rice costs $0.03.
a. Formulate a linear programming model for this problem.
b. Setup the LP model for Excel Solver.
2. A Furniture Company produces chairs and tables from two resources- labor and wood. The
company has 125 hours of labor and 45 board-ft. of wood available each day. Demand for
chairs is limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board-ft. of
wood, whereas a table requires 14 hours of labor and 7 board-ft. of wood. The profit
derived from each chair is $325 and from each table, $120. The company wants to
determine the number of chairs and tables to produce each day in order to maximize profit.
Formulate a linear programming model for this problem.
a. Formulate a linear programming model for this problem.
b. Setup the LP model for Excel Solver.
3. Kroeger supermarket sells its own brand of canned peas as well as several national brands.
The store makes a profit of $0.28 per can for its own peas and a profit of $0.19 for any of
the national brands. The store has 6 square feet of shelf space available for canned peas,
and each can of peas takes up 9 square inches of that space. Point-of-sale records show
that each week, the sales of its own brand is less than twice of the sales of the national
brands. The store wants to know how many cans of its own brand of peas of peas and how
many cans of the national brands to stock each week on the allocated shelf space in order
to maximize profit.
a. Formulate a linear programming model for this problem.
b. Setup the LP model for Excel Solver
4. Set up the LP model for Excel Solver:
Minimize Z=8X1 + 6X2
Subject to
4x1 + 2x2 ≥ 20
-6x1 + 4x2 ≤12
x1 + x2 ≥ 6
x1,x2 ≥ 0
MAT 540 Week 7 Discussion
Discuss sensitivity analysis
Select one (1) of the following topics for your primary discussion posting:
Identify any challenges you have in setting up a linear programming problem in Excel, and
solving it with Solver. Explain exactly what the challenges are and why they are
challenging. Identify resources that can help you with that.
Explain what the shadow price means in a maximization problem. Explain what this tells
us from a management perspective.
MAT 540 Week 7 Homework
Chapter 3
4. Southern Sporting Good Company makes basketballs and footballs. Each product is
produced from two resources rubber and leather. Each basketball produced results in a
profit of $11 and each football earns $15 in profit. The resource requirements for each
product and the total resources available are as follows:
Product
Resource Requirements per Unit
Rubber (lb.) Leather (ft2)
Basketball 2.8 3.7
Football 1.5 5.2
Total resources available 600 900
a. Find the optimal solution.
b. What would be the effect on the optimal solution if the profit for the basketball changed
from $11 to $12?
c. What would be the effect on optimal solution if 400 additional pounds of rubber could
be obtained? What would be the effect if 600 additional square feet of leather could be
obtained?
2. A company produces two products, A and B, which have profits of $9 and $7,
respectively. Each unit of product must be processed on two assembly lines, where the
required production times are as follows:
Product
Resource Requirements per Unit
Line 1 Line 2
A 11 5
B 6 9
Total Hours 65 40
a.Formulate a linear programming model to determine the optimal product mix that will
maximize profit.
b. What are the sensitivity ranges for the objective function coefficients?
c. Determine the shadow prices for additional hours of production time on line 1 and line
2 and indicate whether the company would prefer additional line 1 or line 2 hours.
3. Formulate and solve the model for the following problem:
Irwin Textile Mills produces two types of cotton cloth denim and corduroy. Corduroy is a
heavier grade of cotton cloth and, as such, requires 8 pounds of raw cotton per yard,
whereas denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4
hours of processing time; a yard od denim requires 3.0 hours. Although the demand for
denim is practically unlimited, the maximum demand for corduroy is 510 yards per
month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time
available each month. The manufacturer makes a profit of $2.5 per yards of denim and
$3.25 per yard of corduroy. The manufacturer wants to know how many yards of each
type of cloth to produce to maximize profit. Formulate the model and put it into standard
form. Solve it
a. How much extra cotton and processing time are left over at the optimal solution? Is the
demand for corduroy met?
b. If Irwin Mills can obtain additional cotton or processing time, but not both, which
should it select? How much? Explain your answer.
4. The Bradley family owns 410 acres of farmland in North Carolina on which they grow
corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre
of tobacco costs $210. The Bradleys’ have a budget of $52,500 for next year. The
government limits the number of acres of tobacco that can be planted to 100. The profit
from each acre of corn is $300; the profit from each acre of tobacco is $520. The
Bradleys’ want to know how many acres of each crop to plant in order to maximize their
profit.
a. Formulate the linear programming model for the problem and solve.
b. How many acres of farmland will not be cultivated at the optimal solution? Do the
Bradleys use the entire 100-acre tobacco allotment?
c. The Bradleys’ have an opportunity to lease some extra land from a neighbor. The
neighbor is offering the land to them for $110 per acre. Should the Bradleys’ lease the
land at that price? What is the maximum price the Bradleys’ should pay their neighbor
for the land, and how much land should they lease at that price?
d. The Bradleys’ are considering taking out a loan to increase their budget. For each dollar they
borrow, how much additional profit would they make? If they borrowed an additional
$1,000, would the number of acres of corn and tobacco they plant change?
MAT 540 Week 7 Quiz 3
Question 1
Surplus variables are only associated with minimization problems.
Question 2
A feasible solution violates at least one of the constraints.
Question 3
Graphical solutions to linear programming problems have an infinite number of possible
objective function lines.
Question 4
A linear programming model consists of only decision variables and constraints.
Question 5
If the objective function is parallel to a constraint, the constraint is infeasible.
Question 6
If the objective function is parallel to a constraint, the constraint is infeasible.
Question 7
In a linear programming problem, all model parameters are assumed to be known with certainty.
Question 8
In a linear programming problem, a valid objective function can be represented as
Question 9
Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big
shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300
and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this
week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is
$300 and for each medium shelf is $150. What is the maximum profit?
Question 10
Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big
shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300
and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this
week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is
$300 and for each medium shelf is $150. What is the storage space constraint?
Question 11
The production manager for the Coory soft drink company is considering the production of 2
kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8
hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To
produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4
minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for
diet soft drink are $2.00 per case. What is the objective function?
Question 12
A graphical representation of a linear program is shown below. The shaded area represents the
feasible region, and the dashed line in the middle is the slope of the objective function.
If this is a maximization, which extreme point is the optimal solution?
Question 13
The following is a graph of a linear programming problem. The feasible solution space is shaded,
and the optimal solution is at the point labeled Z*.
Which of the following points are not feasible?
Question 14
The following is a graph of a linear programming problem. The feasible solution space is shaded,
and the optimal solution is at the point labeled Z*.
The equation for constraint DH is:
Question 15
The production manager for the Coory soft drink company is considering the production of 2
kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours
= 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To
produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4
minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for
diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0
cases of diet soft drink, which resources will not be completely used?
Question 16
The following is a graph of a linear programming problem. The feasible solution space is shaded,
and the optimal solution is at the point labeled Z*.
This linear programming problem is a:
Question 17
In a linear programming problem, the binding constraints for the optimal solution are:
5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
Question 18
Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
Find the optimal solution. What is the value of the objective function at the optimal solution?
Note: The answer will be an integer. Please give your answer as an integer without any decimal
point. For example, 25.0 (twenty five) would be written 25
Question 19
A graphical representation of a linear program is shown below. The shaded area represents the
feasible region, and the dashed line in the middle is the slope of the objective function.
What would be the new slope of the objective function if multiple optimal solutions occurred
along line segment AB? Write your answer in decimal notation.
Question 20
Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to: 8x + 5y ≤ 40
0.4x + y ≥ 4
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with the first constraint?
MAT 540 Week 8 Discussion
Practice setting up linear programming models for business applications
Select an even-numbered LP problem from the text, excluding 14, 20, 22, 36 (which are part of
your homework assignment). Formulate a linear programming model for the problem you select.
MAT 540 Week 8 Homework
Chapter 4
1. Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday,
and
she must determine how much beer to stock. Betty stocks three brands of beer- Yodel, Shotz, and
Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:
The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of
$3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past
football games, Betty has determined the maximum customer demand to be 400 gallons of
Yodel,
500 gallons of shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000
gallons of beer; Betty wants to stock up completely. Betty wants to determine the number of
gallons
of each brand of beer to order so as to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
2. As result of a recently passed bill, a congressman’s district has been allocated $3 million for
programs and projects. It is up to the congressman to decide how to distribute the money. The
congressman has decide to allocate the money to four ongoing programs because of their
importance to his district- a job training program, a parks project, a sanitation project, and a
mobile library. However, the congressman wants to distribute the money in a manner that will
please the most voters, or, in other words, gain him the most votes in the upcoming election. His
staff’s estimates of the number of votes gained per dollar spent for the various programs are as
follows.
In order also to satisfy several local influential citizens who financed his election, he is obligated
to
observe the following guidelines:
None of the programs can receive more than 30% of the total allocation
The amount allocated to parks cannot exceed the total allocated to both the sanitation
project and the mobile library.
The amount allocated to job training must at least equal the amount spent on the
sanitation
project.
Any money not spent in the district will be returned to the government; therefore, the
congressman
wants to spend it all. Thee congressman wants to know the amount to allocate to each program to
maximize his votes.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
3. Anna Broderick is the dietician for the State University football team, and she is attempting to
determine a nutritious lunch menu for the team. She has set the following nutritional guidelines
for each lunch serving:
Between 1,300 and 2,100 calories
At least 4 mg of iron
At least 15 but no more than 55g of fat
At least 30g of protein
At least 60g of carbohydrates
No more than 35 mg of cholesterol
She selects the menu from seven basic food items, as follows, with the nutritional contributions
per pound and the cost as given:
The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total
cost per serving.
a. Formulate a linear programming model for this problem and solve.
b. If a serving of each of the food items (other than milk) was limited to no more than a
half
pound, what effect would this have on the solution?
4. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must
determine a schedule for nurses to make sure there are enough of them on duty throughout the
day. During the day, the demand for nurses varies. Maureen has broken the day in to twelve 2-
hour periods. The slowest time of the day encompasses the three periods from 12:00 A.M. to
6:00
A.M., which beginning at midnight; require a minimum of 30, 20, and 40 nurses, respectively.
The demand for nurses steadily increases during the next four daytime periods. Beginning with
the 6:00 A.M.- 8:00 A.M. period, a minimum of 50, 60, 80, and 80 nurses are required for these
four periods, respectively. After 2:00 P.M. the demand for nurses decreases during the afternoon
and evening hours. For the five 2-hour periods beginning at 2:00 P.M. and ending midnight, 70,
70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of
one of the 2-hour periods and works 8 consecutive hours (which is required in the nurses’
contract). Dr. Becker wants to determine a nursing schedule that will meet the hospital’s
minimum requirement throughout the day while using the minimum number of nurses.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
5. The production manager of Videotechnics Company is attempting to determine the
upcoming 5-month production schedule for video recorders. Past production records
indicate that 2,000 recorders can be produced per month. An additional 600 recorders can
be produced monthly on an overtime basis. Unit cost is $10 for recorders produced
during regular working hours and $15 for those produced on an overtime basis.
Contracted sales per month are as follows:
Inventory carrying costs are $2 per recorder per month. The manager does not want any
inventory carried over past the fifth month. The manager wants to know the monthly
production that will minimize total production and inventory costs.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
MAT 540 Week 8 Assignment 1
Assignment 1. Linear Programming Case Study
Your instructor will assign a linear programming project for this assignment according to the
following specifications.
It will be a problem with at least three (3) constraints and at least two (2) decision variables. The
problem will be bounded and feasible. It will also have a single optimum solution (in other
words, it won’t have alternate optimal solutions). The problem will also include a component
that involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet
showing your work.
Writeup.
Your writeup should introduce your solution to the project by describing the problem. Correctly
identify what type of problem this is. For example, you should note if the problem is a
maximization or minimization problem, as well as identify the resources that constrain the
solution. Identify each variable and explain the criteria involved in setting up the model. This
should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective
function and all constraints, including any non-negativity constraints. Then, you should present
the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis
and shadow price.
Excel.
As previously noted, please set up your problem in Excel and find the solution using Solver.
Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the
setup of the model, and the results.
MAT 540 Week 9 Discussion
Discuss characteristics of integer programming problems
Select one (1) of the following topics for your primary discussion posting:
Explain how the applications of Integer programming differ from those of linear
programming. Give specific instances in which you would use an integer programming
model rather than an LP model. Provide real-world examples.
Identify any challenges you have in setting up an integer programming problem in Excel,
and solving it with Solver. Explain exactly what the challenges are and why they are
challenging. Identify resources that can help you with that.
MAT 540 Week 9 Homework
Chapter 5
1. Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However,
the
demand for cabs in the metropolitan area varies dramatically according to time of the day. The
slowest period is between midnight and 4:00 A.M. the dispatcher receives few calls, and the calls
that are received have the smallest fares of the day. Very few people are going to the airport at
that
time of the night or taking other long distance trips. It is estimated that a driver will average $80
in
fares during that period. The largest fares result from the airport runs in the morning. Thus, the
drivers who sart their shift during the period from 4:00 A.M. to 8:00 A.M. average $500 in total
fares, and drivers who start at 8:00 A.M. average $420. Drivers who start at noon average $300,
and
drivers who start at 4:00 P.M. average $270. Drivers who start at the beginning of the 8:00 P.M.
to
midnight period earn an average of $210 in fares during their 8-hour shift.
To retain customers and acquire new ones, Rowntown must maintain a high customer service
level.
To do so, it has determined the minimum number of drivers it needs working during every 4-
hour
time segment- 10 from midnight to 4:00 A.M. 12 from 4:00 to 8:00 A.M. 20 from 8:00 A.M. to
noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M., and 18 from 8:00 P.M. to midnight.
a. Formulate and solve an integer programming model to help Rowntown Cab schedule
its
drivers.
b. If Rowntown has a maximum of only 15 drivers who will work the late shift from
midnight to 8:00 A.M., reformulate the model to reflect this complication and solve it
c. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M., so the company
has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate
the model in (b) to reflect this restriction and solve it.
2. Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is
allowed to
return with a limited number of consumer items not generally available in Cuba. The items,
which
are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells
the
items at highly inflated prices. The weight and profit (in U.S. dollars) of each item are as
follows:
Juan wants to determine the
combination of
items he should pack in his
duffel bag to maximize
his profit. This problem is an example of a type of integer programming problem known as a
“knapsack” problem. Formulate and solve the problem.
3. The Texas Consolidated Electronics Company is contemplating a research and development
program encompassing eight research projects. The company is constrained from embarking on
all
projects by the number of available management scientists (40) and the budget available for
R&D
projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice
versa). Following are the resources requirement and the estimated profit for each project.
Formulate the integer programming model for this problem and solve it using the computer.
4. Corsouth Mortgage Associates is a large home mortgage firm in the southeast. It has a poll of
permanent and temporary computer operators who process mortgage accounts, including posting
payments and updating escrow accounts for insurance and taxes. A permanent operator can
process
220 accounts per day, and a temporary operator can process 140 accounts per day. On average,
the
firm must process and update at least 6,300 accounts daily. The company has 32 computer
workstations available. Permanent and temporary operators work 8 hours per day. A permanent
operator averages about 0.4 error per day, whereas a temporary operator averages 0.9 error per
day.
The company wants to limit errors to 15 per day. A permanent operator is paid $120 per day
wheras
a temporary operator is paid $75 per day. Corsouth wants to determine the number of permanent
and temporary operators it needs to minimize cost. Formulate, and solve an integer programming
model for this problem and compare this solution to the non-integer solution.
5. Globex Investment Capital Corporation owns six companies that have the following estimated
returns (in millions of dollars) if sold in one of the next 3 years:
To generate operating funds, the company must sell at least $20 million worth of assets in year 1,
$25
million in year 2, and $35 million in year 3. Globex wants to develop a plan for selling these
companies
during the next 3 years to maximize return.
Formulate an integer programming model for this problem and solve it by using the computer.
MAT 540 Week 9 Quiz
Question 1
A constraint for a linear programming problem can never have a zero as its right-hand-side
value.
Question 2
Product mix problems cannot have "greater than or equal to" (≥) constraints.
Question 3
In a transportation problem, a demand constraint (the amount of product demanded at a given
destination) is a less-than-or equal-to constraint (≤).
Question 4
Fractional relationships between variables are permitted in the standard form of a linear program.
Question 5
A systematic approach to model formulation is to first construct the objective function before
determining the decision variables.
Question 6
The standard form for the computer solution of a linear programming problem requires all
variables to be to the right and all numerical values to be to the left of the inequality or equality
sign
Question 7
Compared to blending and product mix problems, transportation problems are unique because
Question 8
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,
an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to
$50,000 to invest. The stockbroker suggests limiting the investments so that no more than
$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed
350, whichever is more restrictive. How would this be formulated as a linear programming
constraint?
Question 9
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,
an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates that
stock 1 must not account for more than 35% of the number of shares purchased. Which
constraint is correct?
Question 10
When systematically formulating a linear program, the first step is
Question 11
The production manager for the Softy soft drink company is considering the production of 2
kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8
hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To
produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4
minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for
diet soft drink are $2.00 per case. What is the optimal daily profit?
Question 12
The production manager for the Softy soft drink company is considering the production of 2
kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480
minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a
regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3
gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are
$2.00 per case. What is the time constraint?
Question 13
Let xij = gallons of component i used in gasoline j. Assume that we have two components and
two types of gasoline. There are 8,000 gallons of component 1 available, and the demand
gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint
for component 1.
Question 14
A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear
claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled
croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company
has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for
today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits
are 30 cents each. What is the optimal daily profit?
Question 15
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,
an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to
$50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%.
An appropriate objective function is
Question 16
Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be
shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers).
The company wants to minimize the cost of transporting items between the facilities, taking into
account the demand at the 3 different plants, and the supply at each manufacturing site. The table
below shows the cost to ship one unit between each manufacturing facility and each plant, as
well as the demand at each plant and the supply at each manufacturing facility.
What is the demand constraint for plant B?
Question 17
The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef
feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential
ingredients are contained in the feed, shown in the table below. The table also shows the
minimum daily requirements of each ingredient.
Ingredient
Percent per pound in Feed A
Percent per pound in Feed B
Minimum daily requirement (pounds)
The constraint for ingredient 3 is:
Question 18
A systematic approach to model formulation is to first
Question 19
Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per
gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint
contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and
70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of
ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear
programming to determine the appropriate mix of oil-base and water-base paint to produce to
maximize its total profit. How many gallons of oil based paint should the Quickbrush make?
Note: Please express your answer as a whole number, rounding the nearest whole number, if
appropriate.
Question 20
Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality
of care the pets receive, including well balanced nutrition. The kennel's cat food is made by
mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two
cat foods are as follows:
Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3
ounces of fat per day. What is the cost of this plan? Express your answer with two places to the
right of the decimal point. For instance, $9.32 (nine dollars and thirty-two cents) would be
written as 9.32
MAT 540 Week 10 Discussion
Discussion assignment and transshipment problems
Select one (1) of the following topics for your primary discussion posting:
Explain the assignment model and how it facilitates in solving transportation problems.
Determine the benefits to be gained from using this model.
Identify any challenges you have in setting up an transshipment model in Excel, and
solving it with Solver. Explain exactly what the challenges are and why they are
challenging. Identify resources that can help you with that.
MAT 540 Week 10 Homework
Chapter 6
1. Consider the following transportation problem:
Formulate this problem as a linear programming model and solve it by the using the computer.
2. Consider the following transportation problem:
Solve it by using the computer.
3. World foods, Inc. imports food products such as meats, cheeses, and pastries to the United
States
from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver
the
products to Norfolk, New York and Savannah, where they are stored in company warehouses
before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are
then
distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.)
from
the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports
are
provided in the following table:
The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the
demands
(1000 lb.) at the
distribution centers are as follows:
Determine the optimal shipments between the European ports and the warehouses and the
distribution centers to minimize total transportation costs.
4. The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five
sales
regions. Given their various previous contacts, the sales persons are able to cover the regions in
different amounts of time. The amount of time (days) required by each salesperson to cover each
city is shown in the following table:
Which salesperson should be assigned to each region to minimize total time? Identify the optimal
assignments and compute total minimum time.
MAT 540 Week 10 Quiz 5
Question 1
If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate
constraints in an integer program.
Answer
True
False
Question 2
A conditional constraint specifies the conditions under which variables are integers or real
variables.
Answer
True
False
Question 3
If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional
constraint.
Answer
True
False
Question 4
If we are solving a 0-1 integer programming problem with three decision variables, the constraint
x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint.
Answer
True
False
Question 5
The solution to the LP relaxation of a maximization integer linear program provides an upper
bound for the value of the objective function.
Answer
True
False
Question 6
If we are solving a 0-1 integer programming problem with three decision variables, the constraint
x1 + x2 ≤ 1 is a mutually exclusive constraint.
Answer
True
False
Question 7
In a __________ integer model, some solution values for decision variables are integers and
others can be non-integer.
Answer
total
0 - 1
mixed
all of the above
Question 8
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________
constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
Question 9
Assume that we are using 0-1 integer programming model to solve a capital budgeting problem
and xj = 1 if project j is selected and xj = 0, otherwise.
The constraint (x1 + x2 + x3 + x4 ≤ 2) means that __________ out of the 4 projects must be
selected.
Answer
exactly 2
at least 2
at most 2
none of the above
Question 10
The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff
has 4 different machines that can produce this kind of hose. Because these machines are from
different manufacturers and use differing technologies, their specifications are not the same.
Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.
Answer
Y1 + Y4 ≤ 0
Y1 + Y4 = 0
Y1 + Y4 ≤ 1
Y1 + Y4 ≥ 0
Question 11
The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff
has 4 different machines that can produce this kind of hose. Because these machines are from
different manufacturers and use differing technologies, their specifications are not the same.
Write the constraint that indicates they can purchase no more than 3 machines.
Answer
Y1 + Y2 + Y3+ Y4 ≤ 3
Y1 + Y2 + Y3+ Y4 = 3
Y1 + Y2 + Y3+ Y4 ≥3
none of the above
Question 12
If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________
constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
Question 13
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each
site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.
Restriction 2. Evaluating sites S2 or
S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint(s) for the second restriction
Answer
S2 +S5 ≤ 1
S4 +S5 ≤ 1
S2 +S5 + S4 +S5 ≤ 2
S2 +S5 ≤ 1, S4 +S5 ≤ 1
Question 14
Binary variables are
Answer
0 or 1 only
any integer value
any continuous value
any negative integer value
Question 15
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot
be selected. Which of the alternatives listed below correctly models this situation?
Answer
x1 + x2 + x5 ≤ 1
x1 + x2 + x5 ≥1
x1 + x5 ≤ 1, x2 + x5 ≤ 1
x1 - x5 ≤ 1, x2 - x5 ≤ 1
Question 16
The solution to the linear programming relaxation of a minimization problem will always be
__________ the value of the integer programming minimization problem.
Answer
greater than or equal to
less than or equal to
equal to
different than
Question 17
If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________
constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
Question 18
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each
site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7.
Restriction 2. Evaluating sites S2 or
S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, the constraint for the first restriction is
Answer
S1 + S3 + S7 ≥ 1
S1 + S3 + S7 ≤1
S1 + S3 + S7 = 2
S1 + S3 + S7 ≤ 2
Question 19
Consider the following integer linear programming problem
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 ≤ 30
5x1 + 2x2 ≤ 28
x1 ≤ 8
x1 ,x2 ≥ 0 and integer
Find the optimal solution. What is the value of the objective function at the optimal solution.
Note: The answer will be an integer. Please give your answer as an integer without any decimal
point. For example, 25.0 (twenty-five) would be written 25
Question 20
Max Z = 3x1 + 5x2
Subject to: 7x1 + 12x2 ≤ 136
3x1 + 5x2 ≤ 36
x1, x2 ≥ 0 and integer
Find the optimal solution. What is the value of the objective function at the optimal solution.
Note: The answer will be an integer. Please give your answer as an integer without any decimal
point. For example, 25.0 (twenty-five) would be written 25
MAT 540 Week 11 Discussion
"Reflection to date" Please respond to the following:
• In a paragraph, reflect on what you've learned in this course. Identify the most interesting,
unexpected, or useful thing you’ve learned, and explain how it can be applied to your work or
daily life in some manner.
MAT 540 Week 11 Final Exam
Question 1
In a transshipment problem, items may be transported from destination to destination and from
source to source.
Answer
True
False
Question 2
Excel can be used to simulate systems that can be represented by both discrete and continuous
random variables.
Answer
True
False
Question 3
In an unbalanced transportation model, supply does not equal demand and one set of constraints
uses ≤ signs.
Answer
True
False
Question 4
Fractional relationships between variables are not permitted in the standard form of a linear
program.
Answer
True
False
Question 5
A cycle is an up and down movement in demand that repeats itself in less than 1 year.
Answer
True
False
Question 6
In a total integer model, all decision variables have integer solution values.
Answer
True
False
Question 7
A business owner is trying to decide whether to buy, rent, or lease office space and has
constructed the following payoff table based on whether business is brisk or slow.
The conservative (maximin) strategy is:
Answer
Buy
Rent
Lease
Brisk.
Question 8
Using the minimax regret criterion to make a decision, you
Answer
Construct a table of regrets. Look at the maximum regret for each decision. Select the
decision with the smallest maximum regret.
Look at the worst payoff for each possible decision and select the decision with the largest
worst payoff
Construct a table of regrets. Look at the minimum regret for each decision. Select the
decision with the smallest minimum regret.
Run in circles, scream and shout
Question 9
Using the maximin criterion to make a decision, you
Answer
Construct a table of regrets. Look at the maximum regret for each decision. Select the
decision with the smallest maximum regret.
Look at the worst payoff for each possible decision and select the decision with the largest
worst payoff
Look at the best payoff for each possible decision and select the decision with the largest
best payoff
Consult an astrological table to forecast the state of nature
Question 10
The probability of observing x
successes in a fixed number of trials is a problem related to
Answer
the normal distribution
the binomial distribution
conditional probability
the Poisson distribution
Question 11
Events that cannot occur at the same time in any trial of an experiment are:
Answer
exhaustive
dependent
independent
mutually exclusive
Question 12
Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each
big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs
$50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves
this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf
is $85 and for each medium shelf is $75. What is the constraint on money to invest?
Answer
Max Z = 85B + 75M
100B + 50M ≤ 25000
100B + 50M ≥ 25000
100B + 80M = 18000
Question 13
Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each
big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs
$50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves
this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf
is $85 and for each medium shelf is $75. What is the storage space constraint?
Answer
Max Z = 75B + 85M
100B + 50M ≥ 25000
100B + 80M ≤ 18000
100B + 80M = 18000
Question 14
Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2
What is the sensitivity range for the third constraint, y ≥ 2?
Answer
0 to 4
2 to 5.33
0 to 5.33
4 to 6.33
Question 15
The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two
resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per
week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12
oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat.
Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the
optimal weekly profit?
Answer
$1000
$900
$800
$700
Question 16
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,
an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to
$50,000 to invest.
An appropriate part of the model would be
Answer
15X1 + 47.25X2 +110 X3 ≤ 50,000
MAX Z =15X1 + 47.25X2 + 110X3
X1 + X2 +X3 ≤ 50,000
MAX Z = 50(15)X1 + 50 (47.25)X2 + 50 (110)X3
Question 17
Let xij = gallons of component i used in gasoline j. Assume that we have two components and
two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for
gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint
for component 1.
Answer
x11 + x21 ≤ 8000
x12 + x21 ≥ 8000
x11 + x12 ≤ 8000
x11 + x12 ≥ 8000
Question 18
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________
constraint.
Answer
multiple choice
mutually exclusive
conditional
corequisite
Question 19
The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5
different machines that can produce this kind of hose. Write the constraint that indicates they
have to use at least three of the five machines in their production.
Answer
Y1 + Y2 + Y3 + Y4
+ Y5 ≤ 3
Y1 + Y2 + Y3 + Y4
+ Y5 = 3
Y1 + Y2 + Y3 + Y4
+ Y5 ≥ 3
none of the above
Question 20
The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A,
B, or C.
The constraint that represents the quantity demanded by Customer B is:
Answer
6X1B + 2X2B + 8X3B ≤ 350
6X1B + 2X2B + 8X3B = 350
X1B + X2B + X3B ≤ 350
X1B + X2B + X3B = 350
Question 21
The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A,
B, or C.
The constraint that represents the quantity supplied by DC 1 is:
Answer
4X1A + 6X1B + 8X1C ≤ 500
4X1A + 6X1B + 8X1C = 500
X1A + X1B + X1C ≤ 500
X1A + X1B + X1C ≥500
Question 22
Assume that it takes a college student an average of 5 minutes to find a parking spot in the main
parking lot. Assume also that this time is normally distributed with a standard deviation of 2
minutes. What percentage of the students will take between 2 and 6 minutes to find a parking
spot in the main parking lot?
Answer
11.13%
47.72%
43.32%
62.47%
Question 23
The metropolitan airport commission is considering the establishment of limitations on noise
pollution around a local airport. At the present time, the noise level per jet takeoff in one
neighborhood near the airport is approximately normally distributed with a mean of 100 decibels
and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will
generate a noise level of more than 105 decibels? Note: please provide your answer to 2 places
past the decimal point, rounding as appropriate.
Answer
0.03
0.05
0.07
0.09
Question 24
In the Monte Carlo process, values for a random variable are generated by __________ a
probability distribution.
Answer
sampling from
running
integrating
implementing
Question 25
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Answer
Trend only
Trend plus seasonal
Trend plus irregular
Seasonal
Question 26
A bakery is considering hiring another clerk to better serve customers. To help with this
decision, records were kept to determine how many customers arrived in 10-minute intervals.
Based on 100 ten-minute intervals, the following probability distribution and random number
assignments developed.
Number of
ArrivalsProbability
Random
numbers
6 .1 .01 - .10
7 .3 .11 - .40
8 .3 .41 - .70
9 .2 .71 - .90
10 .1 .91 - .00
Suppose the next three random numbers were .18, .89 and .67. How many customers would
have arrived during this 30-minute period?
Answer
23
24
22
25
Question 27
Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the
forecast for the next period be using simple exponential smoothing?
Answer
36.9
57.5
60.5
62.5
Question 28
Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive
from each booked room is $200. The variable cost per room is $75. How many rooms do they
have to sell each month to break even? (Note: The answer is a whole number. Give the answer
as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms).
Answer
Question 29
Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will
attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to
guarantee that they break even, how much should they charge for each ticket? (Note: Write your
answer with two significant places after the decimal and do not include the dollar “$” sign. For
instance, for five dollars, write your answer as 5.00).
Answer
Question 30
Joseph is considering pursuing an MS in Information Systems degree. He has applied to two
different universities. The acceptance rate for applicants with similar qualifications is 30% for
University X and 60% for University Y. What is the probability that Jim will not be accepted at
either university? (Note: write your answer as a probability, with two decimal places. If
necessary, round to two decimal places. For instance, a probability of 0.252 should be written
as 0.25).
Answer
Question 31
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor
and $30 on each lawn mower, and they sell all they can produce. The time requirements in the
machine shop, fabrication, and tractor assembly are given in the table.
Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period
MAX 30x + 30y
subject to 2 x + y ≤ 60
2 x + 3y ≤ 120
x ≤ 45
x, y ≥ 0
The graphical solution is shown below.
What is the shadow price for fabrication? Write your answers with two significant places after
the decimal and do not include the dollar “$” sign.
Answer
Question 32
Consider the following linear program, which maximizes profit for two products, regular (R),
and super (S):
MAX
50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours)
0.8R + 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$7 Regular = 291.67 0.00 50 70 20
$C$7 Super = 133.33 0.00 75 50 43.75
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67
$E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175
$E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40
If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours),
profits would be reduced by __________. Write your answers with two significant places after
the decimal and do not include the dollar “$” sign.
Answer
Question 33
Kalamazoo Kennels provides overnight lodging for a variety of pets. An attractive feature is the
quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made
by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the
two cat foods are as follows:
Cat Food
Cost/
oz
protien
(%) fat (%)
Pet's Choice 0.35 40 15
Feline Chow 0.32 20 30
Kalamazoo Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least
3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers
with two significant places after the decimal and do not include the dollar “$” sign. For
instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
Answer
Question 34
Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your
answer.
MAX Z = 5x1 + 8x2
s.t. x1 + x2 ≤ 6
5x1 + 9x2 ≤ 45
x1, x2 ≥ 0 and integer
Answer
Question 35
Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. Find P(x
≤ 6). Note: Round your answer, if necessary, to two places after the decimal. Please express
your answer with two places after the decimal.
Answer
Question 36
Ms. Hegel is considering four different opportunities, A, B, C, or D. The payoff for each
opportunity will depend on the economic conditions, represented in the payoff table below.
Investment
Economic Conditions
Poor
(S1)
Averag
e
(S2)
Good
(S3)
Excellent
(S4)
A 80 15 18 47
B 50 75 35 35
C -90 225 -50 12
D 36 25 25 27
Suppose all states of the world are equally likely (each state has a probability of 0.25). What is
the expected value of perfect information? Note: Report your answer as an integer, rounding to
the nearest integer, if applicable
Answer
Question 37
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary
workers. He estimates that net revenues will vary with how well taxpayers comply with the new
tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50
respectively. What is the expected value of perfect information? Do not include the dollar “$”
sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 =
$50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50
= $50,000). Round to the nearest whole number, if necessary.
Answer
Question 38
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary
workers. He estimates that net revenues will vary with how well taxpayers comply with the new
tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50
respectively. What are the expected net revenues for the number of workers he will decide to
hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note:
Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000).
Round to the nearest whole number, if necessary.
Answer
Question 39
Recent past demand for product ABC is given in the following table.
MonthActual
Demand
May 33
June 32
July 39
August 37
The forecasted demand for May, June, July and August were 25, 30, 33, and 38 respectively.
Determine the value of MAD. Note: Please express the result as a number with 2 decimal
places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as
9.15
Answer
Question 40
Consider the following decision tree. The objective is to choose the best decision among the two
available decisions A and B. Find the expected value of the best decision. Do not include the
dollar “$” sign with your answer.
Answer
MAT 540 Complete Course MAT540 Complete Course
Click Link for the Answer:
http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085
http://workbank247.com/q/mat-540-complete-course-mat540-complete-course/22085