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Question

A paper bag manufacturer has determined that the company can sell as many bags as it can produce each month. If it produces x thousand bags in a month, the revenue is
R(x) = 2x2 - 10x + 30 dollars,
and the cost is
C(x) = x2 - 30x + 200 dollars.
Profit is revenue minus cost.
Write a single function Profit P(x) as a function of x.
Determine the profit if the company produces 20,000 bags in one month.
Show and explain your work.

Answer 1

R(x) = 2x² - 10x + 30 dollars

C(x) = x² - 30x + 200 dollars

 

P(x) = R(x)-C(x)

= 2x² - 10x + 30 - (x² - 30x + 200)

= 2x² - 10x + 30 - x² + 30x - 200

= x² + 20x - 170

 

Note that x = # of thousand bags.

This means that for producing 20,000 bags, x=20

 

P(20) = 20² + 20(20) - 170

         = 400 + 400 - 170

         = 800 - 170

         = $630