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?

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.

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