Maximizing Profit 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 = 60 − 0.005x − 0.015y.
The fixed cost attributed to the division is $10,000/week, and the cost for producing 100 3.5-oz size bars and 100 5-oz bath size bars is $8 and $12, 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?
(x, y) =
What is the maximum weekly profit?
$
