Total profit function

Question

In business the total profit P is the difference between the revenue R and the cost C. For x units produced, R(x) = 2000x - 60x^2 and C(x) = 500 + 80x, where R(x) and C(x) are dollar amounts.

a) find the profit function P(x)

b) find the value of x at which the maximum Profit occurs

c) find the maximum profit

THANKS IN ADVANCE!

Answer 1

profit = revenue -cost

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

A. P(x) = 2000x - 60x^2 -(500 + 80x)....Don't forget to distribute the -1

P(x)=2000x-60x^2-500-80x

Always put equations in standard form with highest power first

P(x) = -60x^2+1920x-500

Notice the -60x^2. the graph will be a downward parabola ( an upside down U).

Therefore the max is the vertex of the parabola

B. x-coordinate of the vertex is x=(-b/2a).

-b=-1920, a=-60, 2a=-120

x= (-1920/-120)

x=16

The maximum units is 16.

c. Max profit is 14860

P(16)= -60(16)^2+1920(16) - 500

14860