Johnson's Household Products has a division that produces two sizes of bar soap. The demand equations that relate the prices p and q (in dollars per hundred bars), to the quantities demanded, x and y (in units of a hundred), of the 3.5-oz size bar soap and the 5-oz bath size bar soap are given by p = 80 - 0.01x - 0.005y and q = 50 - 0.005x - 0.015y. The fixed cost attributed to the division is exist10,000/week, and the cost for producing 100 3.5-oz size bars and 100 5-oz bath size bars is exist8 and exist12, respectively. (a) What is the weekly profit function P(x, y)? P(x, y) =
(b) How many of the 3.5-oz size bars and how many of the 5-oz bath size bars should the division produce per week to maximize its profit? 3.5-oz bars 5-oz bars What is the maximum weekly profit?