If C(x) is the cost of manufacturing an amount x of a given product and $12 is the price per unit amount, then the profit P(x) obtained by selling an amount x isP(x) = 12 x − C(x).(Notice that there is a loss if P(x) is negative.) If C(x) = (x − 10)2 + 18, find the maximum profit (which might be negative!).The maximum profit is   dollars.

Question
Asked Oct 21, 2019

If C(x) is the cost of manufacturing an amount x of a given product and $12 is the price per unit amount, then the profit P(x) obtained by selling an amount x is

P(x) = 12 x − C(x).

(Notice that there is a loss if P(x) is negative.)

 If C(x) = (x − 10)2 + 18, find the maximum profit (which might be negative!).

The maximum profit is   dollars.
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Expert Answer

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Step 1

To find the maximum profit, if C(x) is the cost of manufacturing an amount x of a given product and 12$ is the price per unit amount.

Step 2

Given information: the function of profit and cost of manufacturing are given below.

P(x)12x-C(x) and
C(x)(x-10) 18
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P(x)12x-C(x) and C(x)(x-10) 18

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Step 3

For maximum profit derivat...

C(x)=(x-10) 18
P(x)12x-(x-10)+18))
P(x) 12x-C(x)
...1)
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C(x)=(x-10) 18 P(x)12x-(x-10)+18)) P(x) 12x-C(x) ...1)

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Math

Calculus

Derivative

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