COB 300C - The Operations Dimension

Capacity Homework

Problem 2, Chapter 5

A. BEP = FC/(SP-VC)

BEPa = $40,000/($15-$10) = 8000 units

BEPb = $30,000/($16-$12) = 7500 units

B. Same Profit?

5X-40,000=4X-30,000. X=10,000 units

Problem 2, Chapter 5 (cont’d)

C. Demand = 12,000

5(12,000) – 40,000 = $20,000 (alt. A profit)

4(12,000) – 30,000 = $18,000 (alt. B profit)

Problem 9, Chapter 5

Given: 10 hrs. or 600 min. of operating time per day. 250 days x 600 min. = 150,000 min. per year operating time.  

  You would have to buy two "A" machines at a total cost of $80,000, or two "B" machines at a total cost of $60,000, or one "c" machine at $80,000.

Total processing time by machine

Product A B C

1 48,000 64,000 32,000

2 48,000 48,000 36,000

3 30,000 36,000 24,000

4 60,000 60,000 30,000

Total 186,000 208,000 122,000

Problem 10, Chapter 5

10.Total cost for machine A: 186,000 min 60 = 3,100 hrs. x $10 = $31,000 + $80,000 = $111,000

Total cost for machine B: 208,000 min 60 = 3,466.67 hrs. x $11 = $38,133 + $60,000 = $98,133

Total cost for machine B: 122,000 min 60 = 2,033.33 hrs. x $12 = $24,400 + $80,000 = $104,400

SP1. O’Hara Software Company is considering expanding its networking portion of the business. Presently, the company has three networking staff members working at corporate headquarters. O’Hara is examining two options. The first would involve adding six new staff members and building a new facility at the present site. The annual cost of this option, including personnel, is $500,000. The second option involves adding twelve new staff members and building a larger facility at a new location. The annual cost of this option, including personnel, is $1,200,000. O’Hara is looking at the profit potential over the next five years. Management estimates that the present staff can handle up to $2,000,000 in sales over the five-year period, that six additional staff positions allow it to handle up to $6,000,000, and that twelve additional staff positions allow it to handle up to $10,000,000. What do you recommend.

Anticipated Demand Over Five Years Probability

2,000,000 .15

4,000,000 .25

6,000,000 .25

8,000,000 .25

10,000,000 .10

1.00 2 MM Do Nothing .15 2 MM .25 4 MM Add 6 Employees .6 6 MM (new facility at current location) . Add 12 Employees (new facility at new location) .15 2 MM .25 4 MM .25 6 MM .25 8 MM

.10 10 MM

1.00 2 MM Do Nothing .15 2 MM – 500,000 .25 4 MM – 500,000 Add 6 Employees .6 6 MM – 500,000 (new facility at current location) . Add 12 Employees (new facility at new location) .15 2 MM – 1,200,000 .25 4 MM – 1,200,000 .25 6 MM – 1,200,000 .25 8 MM – 1,200,000

.10 10 MM – 1,200,000

1.00 2 MM 2MM Do Nothing .15 2 MM – 500,000 = 1,500,000 .25 4 MM – 500,000 = 3,500,000

4.4MM Add 6 Employees .6 6 MM – 500,000 = 5,500,000 (new facility at current location) .

4.6MM Add 12 Employees (new facility at new location) .15 2 MM – 1,200,000 = 800,000 .25 4 MM – 1,200,000 = 2,800,000 .25 6 MM – 1,200,000 = 4,800,000 .25 8 MM – 1,200,000 = 6,800,000

.10 10 MM – 1,200,000 = 8,800,000

1.00 2 MM 2MM Do Nothing .15 2 MM – 500,000 = 1,500,000 .25 4 MM – 500,000 = 3,500,000

4.4MM Add 6 Employees .6 6 MM – 500,000 = 5,500,000 (new facility at current location) .

4.6MM Add 12 Employees (new facility at new location) .15 2 MM – 1,200,000 = 800,000 .25 4 MM – 1,200,000 = 2,800,000 .25 6 MM – 1,200,000 = 4,800,000 .25 8 MM – 1,200,000 = 6,800,000

.10 10 MM – 1,200,000 = 8,800,000

SP2. Bambino’s Bistro and Restaurant has been open for business for nearly three years, and business is better than ever. Management is contemplating another restaurant in a nearby suburb. Their plan is to build a restaurant to serve about 180 people per hour. The restaurant will have a game room, a bar area, and a dining area. From previous experience, management anticipates that 25 percent of the customers will come primarily for the game room, 20 percent for the bar, and 55 percent for dining. The average stay is 75 minutes per customer, and approximately 2.2 people arrive per car. Typically, very few people in the game room order dinner. Each meal prepared per hour requires 4.5 square feet of kitchen area. It is very difficult to push the occupancy for the bar above 90 percent and for the dining area above 90 percent because some parties of two or three are seated at tables for four. The 180 people per hour is the arrival rate. a. How large should the parking area, bar area, game room, dining area,

and kitchen area be to serve 180 people per hour? b. What would happen to the capacities of the areas if the system capacity

is to be increased by 10 percent?

AREA CAPACITY Parking (180 people/hr.)(1.25 hrs.)/2.2 people/car = 102 cars Game Room (180 people/hr.)(.25)(1.25 hrs.)/(1 people/seat) = 56 seats Bar (180 people/hr.)(.20)(1.25 hrs.)/(.9 people/seat) = 50 seats Dining (180 people/hr.)(.55)(1.25 hrs.)/(.9 people/seat) = 138 seats Kitchen (180 people/hr.)(.25)(0 meals/person) + (180 people/hr.)(.20)(.3 meals/person) + (180 people/hr.)(.55)(1 meal/person) = 110 meals

110 meals requires (110 meals)(4.5 s.f./meal) = 494 square feet

Supplement # 5 (page 211)

Small demand (.4) $1.0

Do Nothing $1.3

Medium Demand (.5) Expand $1.3

Do Nothing $1.5

Large Demand (.1) Expand $1.6

Subcontract Build $1.8 Do Nothing $0.7 Small demand (.4) Other Use #1 $1.5 Other Use #2 $1.0 Expand Medium demand (.5) $1.6 Do Nothing $1.6

Large demand (.1) Subcontract $1.5 Build $1.7 Build Do Nothing ($0.9) Small demand (.4) Other Use #1 $1.4 Other Use #2 $1.0 Do Nothing $1.0 Medium demand (.5) Other Use #1 $1.1 Other Use #2 $0.9 Large demand (.1) $2.4

Small demand (.4) $1.0

Do Nothing $1.3

Medium Demand (.5) Expand $1.3

Do Nothing $1.5

Large Demand (.1) Expand $1.6

1.23 MM Build $1.8 Subcontract Do Nothing $0.7 Small demand (.4) Other Use #1 $1.5 Other Use #2 $1.0

1.57 MM Expand Medium demand (.5) $1.6 Do Nothing $1.6

Large demand (.1) Subcontract $1.5

1.35 MM Build $1.7 Build Do Nothing ($0.9) Small demand (.4) Other Use #1 $1.4 Other Use #2 $1.0 Do Nothing $1.0 Medium demand (.5) Other Use #1 $1.1 Other Use #2 $0.9 Large demand (.1) $2.4

a Small demand (.4) $1.0

Do Nothing $1.3

Medium Demand (.5) Expand $1.3

Do Nothing $1.5

Large Demand (.1) Expand $1.6

1.23 MM Build $1.8 Subcontract Do Nothing $0.7 Small demand (.4) Other Use #1 $1.5 Other Use #2 $1.0

1.57 MM Expand Medium demand (.5) $1.6 Do Nothing $1.6

Large demand (.1) Subcontract $1.5

1.35 MM Build $1.7 Build Do Nothing ($0.9) Small demand (.4) Other Use #1 $1.4 Other Use #2 $1.0 Do Nothing $1.0 Medium demand (.5) Other Use #1 $1.1 Other Use #2 $0.9 Large demand (.1) $2.4

Problem # 12 (page 214)

A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be $400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.

If a large facility is built and demand is high, the estimated net present value is $800,000. If demand turns out to be low, the net present value will be negative $10, 000.

The probability that demand will be high is estimated to be .60, and the probability of low demand is estimated to be .40.

Analyze using a tree diagram.

400,000 .4

low .6 50,000

Small high maintain . expand 450,000 Large low -10,000 .4 . high 800,000

.6

400,000 .4

low .6 50,000

Small high maintain . expand 450,000 Large low -10,000 .4 . high 800,000

.6

400,000 .4

low

430,000 .6 50,000 Small high maintain

. expand 450,000

476,000 Large low -10,000 .4 . high 800,000

.6

400,000 .4

low

430,000 .6 50,000 Small high maintain

. expand 450,000

476,000 Large low -10,000 .4 . high 800,000

.6