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olga nikolaevna [1]
2 years ago
8

Suppose a computer manufacturer has the total cost function

Mathematics
1 answer:
S_A_V [24]2 years ago
7 0

Answer:

(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) \geq 0

300 x -3600  \geq 0

300 x  \geq 3600

x  \geq 3600/300

x  \geq 12

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

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