Question

A company produces x units of a product per month, where c(x) represents the total cost and r(x) represents the total revenue for the month. The functions are modeled by c(x)=300x+250 and r(x)=-0.5x^2+800x-100.

The profit is the difference between revenue and cost where p(x)=R(x)-C(x).
What is the total profit p(x), for the month?

Answer 1

The total profit P(x) or the month is
`P(x)=-0.5x^2+500x-350`.

Explanation:

A company produces x units of a product per month.

The total cost represents by the function C(x).

`C(x)=300x+250`

The total revenue represents by the function R(x).

`R(x)=-0.5x^2+800x-100`

The profit is the difference between revenue and cost.

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

`P(x)=-0.5x^2+800x-100-(300x+250)`

`P(x)=-0.5x^2+800x-100-300x-250`

Combine like terms.

`P(x)=-0.5x^2+(800x-300x)+(-100-250)`

`P(x)=-0.5x^2+500x-350`

Therefore, the total profit P(x) or the month is
`P(x)=-0.5x^2+500x-350`.