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) = 334 − 2x. The cost of producing x widgets is given by C(x) = 1,687 + 18x. 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.

a) The revenue is the product of the price and the number of items. Given that p(x) = 334 − 2x and the number of widget is x, hence the revenue R(x) is given as:

R(x) = x × p(x) = x × 334 − 2x = 334x - 2x²

b) The maximum revenue is gotten by setting the first derivative of the revenue to 0, hence:

R'(x) = 334 - 4x

334 - 4x = 0

4x = 334

x = 334/4

x = 83.5

x ≈ 84

84 widgets are needed for maximum revenue

c) R(4) = 334(84) - 2(84²) = 13944

The maximum revenue is $13944