Question

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?

Answer 1

Answer:

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.

Answer 2

There is no maximum profit,  if C(x) = cx and c < 10

What is profit?

Revenue is the total amount of money made by selling x number of items. Cost is the total amount of money spent on production.

Profit = Revenue - Profit

From the question, Revenue = 10x, Cost = C(x)

Profit = 10x - C(x)

When C(x) = cx; c  < 10, let x = 9:

Profit = 10x - 9x = x

There is no maximum profit,  if C(x) = cx and c < 10

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