Engineering Economic Analysis

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Problems 55

Total cost, System I:y=0.9Ox+ 1.0

Total cost, System II:

y=O.lOx+ 5.0

5 10

Maps Dispensed per year (thousands)

2-5

(g)For what range of annual number of maps dis-

pensed is System ITrecommended?

(h)At 3000 maps per year, what are the marginaland

average map costs for each system?

Mr. Sam Spade, the president of Ajax, recently read

in a report that a competitor named Bendix has the

following relationship between cost and production

quantity:

c = $3,000,000 - $18,000Q+$75Q2

where C = total manufacturing cost per year and

Q=number of units produced per year.

A newly hired employee, who previously

worked for Bendix, tells Mr. Spade that Bendix is

now producing 110 units per year. If the selling price

remains unchanged, Sam wonders if Bendix is likely

to increase the number of units produced per year, in

the near future.He asks you to look at the information

and tell him what you are able to deduce from it.

2-6 A privately owned summer camp for youngsters has

the following data for a 12-week session:

Charge per camper

Fixed costs

Variable cost per camper

Capacity

$120 per week

$48,000 per session

$80 per week

200 campers

(a)Develop the !Ilathematical relationships for total

cost and total revenue.

(b)What is the total number of campers that will

allow the camp tojust break even?

(c) What is the profit or loss for the 12-week session

if the camp operates at 80% capacity?

2-7 Two new rides are being compared by a local amuse-

ment park in terms of their annual operating costs.

The two rides are assumed to be able to generate the

same level of revenue (and thus the focus on costs).

The Thmmy Thgger has fixed costs of $10,000 per

year and variable costs of $2.50 per visitor. The Head

Buzzer has fixed costs of $4000 per year, and variable

costs of $4 per visitor. Provide answers to the follow-

ing questions so the amusement park can make the

needed comparison.

(a) Mathematically determine the breakeven number

of visitors per year for the two rides to have equal

annual costs.

(b) Develop a graph that illustrates the following:

(Note:Put visitors per year on the horizontal axis

and costs on the vertical axis.)

·Accurate total cost lines for the two alternatives

(show line, slopes, and equations).

·The breakeven point for the two rides in terms

of number of visitors.

·The ranges of visitors per year where each

alternative is preferred.

2-8 Consider the accompanying breakeven graph for an

investment, and answer the following questions as

they pertain to the graph.

$40

$35

....." , $30

~x $25

'-' $20

E

'0Q

,.,.

,.

Total Revenue,.",.

,.,.

,.,.

....,.

,..,

$15 ,.,.,."

$10- ,.",,."

,.

$5 ,.,.,.,.

$0o,. 250 500 750 1000 1250

Output (units/year)

(a)Give the equation to describe total revenue forx

units per year.

(b)Give the equation to describe total costs forx

units per year.

(c) What is the "breakeven" level ofx in terms of

costs and revenues?

(d) If you sell 1500 units this year, will you have a

profit or loss? How much?

2-9 Quatro Hermanas, Inc. is investigating implement-

ing some new production machinery as part of its

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$10

$8

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!arI.I $6

6

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$2

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