Question

Total profit P is defined as total revenue R minus total cost​ C, and is given by the function P(x)=R(x)−C(x). Find the total profit​ P(x) when ​R(x)=126.98x−0.5x2 and C(x)=3809.40+0.7x2.

Answer 1

Given:

The revenue function is

$R(x)=126.98x-0.5x^2$

The cost function is

$C(x)=3809.40+0.7x^2$

To find:

The profit function.

Solution:

We know that, the total profit P is defined as total revenue R minus total cost​ C.

So, the profit function is

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

$P(x)=126.98x-0.5x^2-(3809.40+0.7x^2)$

$P(x)=126.98x-0.5x^2-3809.40-0.7x^2$

$P(x)=-3682.42-1.2x^2$

Therefore, the profit function is $P(x)=-3682.42-1.2x^2$.