Question

WidgCo is a company that produces and sells widgets. Let p denote the price per widget (measured in dollars), and let x be the monthly demand for widgets. WidgCo's marketing department determines that p and x are related by the following demand equation: p(x) = 211 − 5x. The cost of producing x widgets is given by C(x) = 1,401 + 16x. Construct the revenue function, R(x). Find the production level that will result in the maximum revenue. Find the maximum monthly revenue. Enter your answer to part c in the box below. Round your answer to the nearest cent.

Answer 1

the revenue function = x · P(x) - C(x) = x · (211 − 5x) - (1,401 + 16x) = 211x - 5x² - 1,401 - 16x = -5x² + 211x - 16x - 1,401

R(x) = -5x² + 195x - 1,401

maximum revenue will be obtained for R'(x)

R'(x) = 2 · -5x + 195 = -10x + 195 = 0

195 = 10x

x = 19.5

the production level that yields a maximum profit should be 19.5

maximum monthly revenue

R(x) = -5·19.5² + 195·19.5 - 1,401 = -1,901.25 + 3,802.50 - 1,401 = $500.25