Definition:ENGINEERING ECONOMY is a discipline

concerned with the systematic evaluation of the costs and benefits of the proposed business projects and ventures. Its objective is to choose which among the alternative course of action will give the maximum benefit at the least cost.

Engineering Economy, therefore involves the application of definite laws of Economics, theories of investment and business practices to engineering problems involving cost. It also involves the study of cost features and other financial data and their applications in the field of engineering as basis for decision.

COST CONCEPTS

DEMAND – is the quantity of a certain commodity that is bought at a certain price at a given place and time.

SUPPLY – is the quantity of a certain commodity that is offered for sale at a certain price at a given place and time.

FIXED COST – are costs that do not vary in proportion to the quantity of output.

VARIABLE COST – are costs that vary in proportion to quantity of output.

BREAK EVEN POINT – is the level of production at which revenue is exactly equal to total costs

LAW OF SUPPLY

The supply of the commodity varies directly as the price of the commodity, though not proportionately

Supply

price

LAW OF DEMAND

The demand for a commodity varies inversely as the price of the commodity, though not proportionately

Demand

price

LAW OF DEMAND AND SUPPLY

Under conditions of perfect competition, the price at which any given product will be supplied and purchased is the price that will result in the supply and the demand being equal.

Quantity

price

The relationship between price and demand can be expressed as a line

Where a is the intercept on the price (p)axis and –b is the slope.

p = a - bD

price

Demand (D)

TOTAL REVENUE – VOLUME RELATIONSHIP

Volume (D)

Peak point – represents theMaximum revenueT

OTAL

Revenue

D'

Demand that maximizes Total Revenue

2

)(

bDaDTR

or

DbDaTR

pDTR

COST - VOLUME RELATIONSHIPTotal Cost

Fixed Cost

Variable CostCost

Volume (D)

TFCvcDTC

TFCTVCTC

COMBINATION OF COST - VOLUME & REVENUE VOLUME RELATIONSHIP

Volume (D)

Represents theMaximum ProfitC

ost

Revenue

D *

Demand that maximizes Total Profit

or Total Cost

b

vcaD 2

*

Formulas:

Price:

Total Revenue:

Total Cost :

bDap

2

)(

bDaDTR

or

DbDaTR

pDTR

TFCvcDTC

TFCTVCTC

Profit:

Demand that maximizes Revenue

Demand that maximizes Profit

(Optimum Profit)

TFCDvcabDP

TFCvcDDbDaP

TFCvcDpDP

TCTRP

)(

)(

)(

2

ba

D2

b

vcaD 2

*

Break even points: Profit = 0

TFCDvcabD

TFCDvcabDP

TFCvcDDbDaP

TFCvcDpDP

TCTRP

)(0

)(

)(

)(

2

2

)(2

))((4)()( 2'

b

TFCbvcavcaD

I. COST CONCEPTS

B: Price is not constant

Break even point:

Loss

PROFIT

Volume (D)

Revenue

COST

or

Break Even Pointwhere TR=TC

vcp

TFCD

'

vcp

TFCD

'

Examples:1. A company produces an electronic timing switch

that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost is $73,000 per month, and the variable cost is $83 per unit. The selling price per unit is p = $180 - 0.02D. For this situation a.) determine the optimal volume for this product and confirm that a profit occurs (instead of a loss) at this demand; and b.) find the volumes at which break-even occurs; that is, what is the range of profitable demand

Examples2. A large semiconductor plant has approximately 95% of sales

due to a single circuit design. The plant can therefore be considered to produce 3,000,000 printed circuit boards (PCBs) per year. Presently, the plant is operating at 60% of capacity. The selling price of the PCB is

p = $19.25 – (10- 6 )D, and the variable cost per PCB is $15.75. At zero output, the plants annual fixed costs are $1,000,000 and are approximately constant up to the maximum production quantity per year.

a.What the percentage of production capacity that will result in optimal operation? What is the maximum profit or minimum loss at this optimal volume?

b.Determine at what demand(s) breakeven occurs in the operation

Examples3. A company has established that the

relationship between the sales price for one of its products and the quantity sold per month is approximately D = 780 – 10p units. The fixed cost is $800 per month, and the variable cost is $30 per unit produced. What number of units should be produced per month and sold to maximize net profit? What is the maximum profit per month? Determine the range of profitable demand.

Examples:4.A manufacturing company leases for $100,000 per year a

building that houses its manufacturing facilities. In addition, the machinery in the building is being paid for installments of $20,000 per year. Each unit of product produced costs $15 in labor and $10 in materials and can be sold for $40.

a.How many units per year must be sold for the company to break even?

b. If 10,000 units per year are sold, what is the annual profit?

c. If the selling price is lowered to $35 per unit, how many units must be sold each year for the company to earn a profit of $60,000 per year?

Examples:4. The annual fixed costs for a plant are P100,000

and the variable costs are P140,000 at 70%utilization of available capacity with net sales of P280,000. What is the break even point in units of production if the selling price per unit is P40.

6. Suppose we know that p=1,000 – D/5, where p = price in dollars and D = annual demand. The total cost per year can be approximated by $1,000 + 2D2 .

a.Determine the value of D that maximizes profit.

b.Show that in part(a) profit has been maximized rather than minimized.

6. The fixed cost for a steam line per meter of pipe is $450X + $50 per year. The cost for loss of heat from the pipe per meter is $4.8/X1/2 per year. Here X represents the thickness of insulation in meters and X is a continuous design variable.a. What is the optimum thickness of the insulation?b. How do you know that your answer in (a) minimizes total cost per year?

7. A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week.

a.What is the optimum number of units the defense contractor should produce in order to maximize profit per week?

b.What is the profit if the optimum number of units are produced?

Seatwork:1. A company has determined that the price and that

monthly demand of one of its products are related by the equation

The associated fixed costs are $1,125/month, and the variable costs are $100/unit.

a. What is the optimal number of units that should be produced and sold each month to maximize profit?

b. What is the optimal number of units to maximize revenue and the maximum revenue?

c. What are the break even points?

)400( pD

2. A plant operation has fixed cost of $2,000,000 per year, and its output capacity is 100,000 electrical appliances per year. The variable cost is $40 per unit, and the product sells for $90 per unit.

a) What is the annual break even volume of this product?

b) Compare annual profit when the plant is operating at 90% capacity with the plant operation at 100% capacity. Assume that the first 90% of capacity output is sold at $90 per unit and that the remaining 10% of production is sold at $70 per unit.

3. A manufacturer is currently selling 1000 decorative lamps a month to the retailers at a price of P800 per lamp. Its estimates that for each P50 increase in the price will sell 20 fewer lamps each month. The manufacturer’s cost consists of a fixed overhead of P300,000/ month plus P300 per lamp for labor and materials.

a.Set up the total cost function

b.Set up the demand function

c. Find the Break Even points

d.Find the volume that will maximize profit

e.What is the maximum profit?

f. What is the volume of sales that will maximize your sales revenue?

4. Bragg & Stratton Company manufactures a specialized motor for chain saws. The company expects to manufacture and sell 30,000 motors in year 2001. It can manufacture an additional 10,000 motors without adding new machinery and equipment. Its projected total costs for the 30,000 units are as follows:Direct Materials $150,000Direct Labor 100,000Manufacturing Overhead:

Variable Portion 100,000Fixed Portion 80,000

Selling and Administrative costs:Variable Portion 180,000Fixed Portion 70,000

The selling price for the motor is $80.a. What is the total manufacturing cost per unit if 300,000 motors are produced?b. What is the total manufacturing cost per unit if 40,000 motors are produced?c. What is the break even price on the motors?

BREAK – EVEN ANALYSIS, TWO ALTERNATIVES

Industry is faced with certain situations where two or more alternatives can be considered. When the cost for two alternatives is affected by a common decision variable, there may exist a value of the variable for which the two alternatives will incur equal cost. This value is known as the break-even cost. Below this cost, one method will be more economical, and above this cost, the other will prove to be better economically.

TCATCB

Total Cost

D’ Volume (D) TCA = TCB

Examples1. Two manufacturing methods are being

considered. Method A has a fixed cost of P5,000 and a variable cost of P50. Method B has a fixed cost of P2500 and a variable cost of 150. For what production volume would one prefer (a) Method A, and (b) Method B?

2. Two companies are engaged in the manufacture of shirts. Company A, using mostly handwork, has a fixed cost monthly expense of P45,000 and a variable cost of P15.00 per shirt. Company B has been able to mechanize most of its operations, and it finds its fixed monthly expenses are P80,000 and the variable cost per shirt is P12.50.

a. How many shirts should be manufactured by each month so that the total cost will be the same for the two companies?

b. If each shirt sells for P32.00 to the retailers, determine the monthly gross profit for each company.