Question

75 9. A marketing researcher has determined that when a product sells at a dollars per unit, the number of units sold per week is given by the function q = - + 80(5m - 2) where m>O is the total manufacturing cost in dollars per unit and m < x < 5m. 2 m (a) Find the profit function P(x) (in dollars per week) and simplify it. (5 points) (b) Use calculus to find the selling price x that maximizes weekly profit. Sufficiently justify your solution. [6 points] (c) Use your answer to part (b) to determine the manufacturing cost m that yields a maxi- mum weekly profit of 3, 455 dollars. [4 points)