Question

For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−90)^2+4,050 . The maximum capacity of the company is 140 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!\Assuming that the company sells all that it produces, what is the profit function?P(x)= i just need the profit function

Answer 1

The profit function P(x) is the revenue function R(x) minus the cost function C(x). Thus:

`\begin{gathered} P(x)=R(x)-C(x) \\ . \\ \begin{cases}R(x)={-0.5(x-90)^2}+4050 \\ C(x)={40x+150}\end{cases} \\ . \\ P(x)=-0.5(x-90)^2+4050-(40x+150) \end{gathered}`

And solve:

`P(x)=-0.5(x^2-180x+8100)+4050-40x-150=-0.5x^2+90x-4050-40x-150=-0.5x^2+50x-150`

Thus, the profit function is:

`P(x)=-0.5x^2+50x-150`