Question

The monthly revenue Rachieved by seling x wristwatches is figured to be R(x) = 79x - 0.2x”The monthly cost of selling x wristwatches is C(x) = 2x + 1700 (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x) = R(x) - CIX). What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (a) The firm must sell 190 wristwatches to maximize revenue (Round to the nearest integer as needed.) The maximum revenue is $7801.25 (Round to two decimal places as needed.) (b) The profit function is P(x) - (x) - (x) (Type an expression using x as the variable.) (c) The firm must sewristwatches to maximize profit (Round to the nearest Integer as needed.) The maximun profit is $ (Round to two decimal places as needed.) (d) Why do the answer found in part (a) and part (c) differ? Choose the correct answer below. O A. The parts differ because part (c) uses the profit function which is equal to the product of the revenue function and the cost function OB. The parts differ because part (a) uses the profit function which is equal to the difference of the revenue function and the cost function. OC. The parts differ because part (e) uses the revenue function which is equal to the sum of the profit function and the cost function. OD. The parts differ because part (a) uses the revenue function which is equal to the sum of the profit function and the cost function. Explain why a quadratic function is a reasonable model for revenue. Choose the correct answer below. O A. Revenue is the profit of the item times the number of units actually sold. So the revenue, R, is a quadratic function of the price p. OB. Revenue is the selling price of the item times the number of units actually sold. So the revenue, R, is a quadratic function of the price p. OC. Revenue is the profit of the item plus the number of units actually sold. So the revenue, R, is a quadratic function of the price p. OD. Revenue is the solling price of the item plus the number x of units actually sold. So the revenue, R, is a quadratic function of the price p.