Question

Jorge’s new company, Jorge’s Widgets, has a Total Cost function, C(x)=10x^2-60x+2500 and a Revenue function, R(x) = 500x after producing and selling x widgets. Find the Profit function, P(x), for Jorge’s company.

A. P(x) = 10x^2 - 60x - 2000
B. P(x) = 10x^2 - 60x + 2000
C. P(x) = 10x^2 + 60x - 2000
D. P(x) = 10x^2 + 60x + 2000

Answer 1

To find the profit function, subtract the Total Cost function from the Revenue function. In this case, the profit function is P(x) = -10x^2 + 560x - 2500.

Step-by-step explanation:

The profit function for Jorge's company can be found by subtracting the Total Cost function from the Revenue function. So, P(x) = R(x) - C(x).

Given that the Total Cost function is C(x) = 10x^2 - 60x + 2500 and the Revenue function is R(x) = 500x, we can substitute these values into the profit function formula.

P(x) = 500x - (10x^2 - 60x + 2500)
= 500x - 10x^2 + 60x - 2500
= -10x^2 + 560x - 2500