Question

. A mathematical organization publishes a math journal each month. Suppose that the function C(x) = 6x² + 20x represents the estimated monthly cost, and R(x) = –0.4x³ + 38x²– 25x + 150 represents the estimated monthly revenue, where x is in hundreds of subscribers. The profit is the difference between the revenue and the cost.What is the profit function, P(x)

Answer 1

Case: Polynomials (Cost and Revenue)

Given:

Monthly cost

C(x) = 6x² + 20x

Monthly revenue

R(x) = –0.4x³ + 38x²– 25x + 150

Required: What is the profit function, P(x)

Method:

The profit is the difference between the revenue and the cost.

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

P(x)= (–0.4x³ + 38x²– 25x + 150) - (6x² + 20x)

P(x)= –0.4x³+(38x² - 6x²)+(– 25x- 20x) + 150

P(x)= –0.4x³ + 32x² - 45x + 150

Final answer:

The expression for the profit function, P(x) is:

P(x)= –0.4x³ + 32x² - 45x + 150