# 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

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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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.

Step 3

For maximum profit derivat...

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### Derivative 