AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost

Question

AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost of $48,000 and a production cost of $8 for each timer manufactured. The timers sell for $13 each.

(a) What is the cost function C(x)?
C(x) =  

8x+48,000

  

(b) What is the revenue function R(x)?
R(x) =  

13x

  

(c) What is the profit function P(x)?
P(x) =  

13x(8x+48,000)

(d) Compute the profit (loss) corresponding to production levels of 4000, 5000, and 12,000 timers, respectively. (Input a negative value to indicate a loss.)

Explanation / Answer

given fixed cost =$48000

Production cost per timer =$ 8

selling price of a timer =$13

let X is number of units of timer

a)

Cost function

$48000 fixed and $ 8 for per timer so

C(X) =48000+8x

b)

selling price =$13 per timer so

R(X) =13X

c)

Profit = Revenue -cost

=13X-(48000+8X)

=5X-48000

P(X) =5X-48000

d)

as P(X) =5X-4800

1) X=4000

P(X) =5*4000-48000=20000-48000=-($28000)

2)

X=5000

P(X) =5*5000-48000 =25000-48000=-($23000)

3)

X=12000

P(X) =5*12000-48000 =60000-48000=$12000

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