If C (x) is the cost of manufacturing an amount x of a given product and $10 is the price per unit amount, then the profit P (x) obtained by selling an amount x is P (x) = 10 x - C (x). (Notice that there is a loss if P (x) is negative.) a. If C (x) = cx and c < 10, is there a maximum profit?

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13 July, 08:45

If C (x) is the cost of manufacturing an amount x of a given product and $10 is the price per unit amount, then the profit P (x) obtained by selling an amount x is P (x) = 10 x - C (x). (Notice that there is a loss if P (x) is negative.) a. If C (x) = cx and c < 10, is there a maximum profit?

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August · Answer 1

No, There is not maximum profit

Explanation:

C (x) = cx

P (x) = 10x - C (x)

= 10x - cx

= x (10 - c)

if c<10 then:

10 - c >0

m>0 for m = 10 - c

P (x) = mx where. m>0

so this is a straight line with a positive slope, m.

therefore, theres is no maximum profit since as x - > infinity, P (x) = mx - > infinity as well.