Use the revenue and cost functions below to answer part A B

Use the revenue and cost functions below, to answer part (A), (B), and (C). R(x) = 75x - 3x^2 1 lessthanorequalto x lessthanorequalto 20 C(x) = 120 + 16x 1 lessthanorequalto x lessthanorequalto 20 (A) What is the profit function? P(x) = What is the domain of the profit function? A. [1, 20] B. [0, 20] C. [0, 160] D. [0, 75] (B) Complete the table. Click to select your answer(s). (C) Choose the best graph of the profit function using the points from the table.

Solution

Given

Revenue Function R(x) = 75x - 3x²

Cost function C(x) = 120 + 16x

Profit Function P(x) = Revenue - Cost

                     = 75x - 3x² - (120 + 16x)

                     = 75x - 3x² - 120 - 16x                     // minus sign gets distributed over the bracket

                    = 59x - 3x² - 120

C)

P(x) = 59x - 3x² - 120                    

This represents a parabola.

The coefficient of x² is negative therefore it will be a downward parabola.

Ans is option (D)