Engineering Economic Analysis

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Problems 25

the clerk's wage and other incremental operating

costs, is $10 per hour. To maximize profit, when

should the store be opened, and when should it be

closed?

Jim Jones, a motel owner, noticed that just down the

street the "Motel 36" advertises a $36-per-night room

rental rate on its sign. As a result, this competitor rents

all 80 rooms every day by late afternoon. Jim, on the

other hand, does not advertise his rate, which is $54

per night, and he averages only a 68% occupancy of

his 50 rooms.

There are a lot of other motels nearby, but only

Motel 36 advertises its rate on its sign. (Rates at the

other motels vary from $48 to $80 per night.) Jim

estimates that his actual incremental cost per night

for each room rented, rather than remaining vacant,

is $12. This $12 pays for all the cleaning, launder-

ing, maintenance, utilities, and so on. Jim believes

his eight alternatives are:

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Alternative

Resulting

Occupancy Rate

1

2

3

4

Advertise

and Charge

$35 per night

42 per night

48 per night

54 per night

Do Not Advertise

and Charge

$48 per night

54 per night

62 per night

68 per night

100%

94

80

66

70%

68

66

56

5

6

7

8

What should Jim do? Show how you reached your

conclusion.

A firm is planning to manufacture a new product.

The sales department estimates that the quantity that

can be sold depends on the selling price. As the sell-

ing price is increased, the quantity that can be sold

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decreases. Numerically they estimate:

P=$35.00 - 0.02Q

where P=selling price per unit

Q=quantity sold per year

On the other hand, the management estimates that

the average cost of manufacturing and selling the

product will decrease as the quantity sold increases.

They estimate

C=$4.00Q+ $8000

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where C =cost to produce and sell Qper year

The firm's management wishes to produce and sell

the product at the rate that will maximize profit, that

is, where income minus cost will be a maximum.

What quantity should the decision makers plan to

produce and sell each year? (Answer:775 units)

A manufacturing firm has received a contract to as-

semble 1000units of test equipment in the next year.

The firm must decide how to organize its assembly

operation. Skilled workers, at $22 per hour each,

could be assigned to individually assemble the test

equipment. Each worker would do all the assembly

steps, and it would take 2.6 hours to complete one

unit. An alternate approach would be to set up teams

of four less skilled workers (at $13 per hour each) and

organize the assembly tasks so that each worker does

part of the assembly. The four-man team would be

able to assemble a unit in one hour. Which approach

would result in more economically assembly?

A grower estimates that if he picks his apple crop

now, he will obtain 1000 boxes of apples, which he

can sell at $3 per box. However, he thinks his crop

will increase by 120 boxes of apples for each week

he delays picking, but that the price will drop at a rate

of l5~ per box per week; in addition, he estimates

approximately 20 boxes per week will spoil for each

week he delayspicking. When should he pick his crop

to obtain the largest total cash return? How much will

he receive for his crop at that time?

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