Suppose a computer manufacturer has the total cost function
C(x) = 84x + 3600
(in dollars) and the total revenue function
R(x) = 384x
(in dollars).
(a) What is the equation of the profit function P(x) (in dollars) for this commodity?
P(x) =

(b) What is the profit (in dollars) on 340 items?
P(340) = $

(c) How many items must be sold to avoid losing money?
x =
items

(a)  P(x) = 300 x - 3600

(b)  P(340) = $ 98400

(c)  At least 12 items must be sold to avoid losing money.

Step-by-step explanation:

Part (a):

The Profit function is the difference between the revenue function (R(x)) and the Cost (C(x)) function:

P(x) = R(x) - C(x)

P(x) = 384 x - [84 x + 3600]

P(x) = 384 x - 84 x - 3600

P(x) = 300 x - 3600

Part (b):

The profit on 340 items is:

P(340) = 300 (340) - 3600

P(340) = 102000 - 3600

P(340) = $ 98400

Part (c):

To avoid losing money, the profit P(x) has to be larger or equal than zero. That is:

P(x) 0

300 x -3600   0

300 x   3600

x   3600/300

x   12

So at least 12 items must be sold to avoid losing money.