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)? Px, v) - -0.01x² – 0.015y2 + 72x + 48y – 0.010xy – 10000 (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, v) - (| What is the maximum weekly profit? $ 122480

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Chapter4: Complex Numbers
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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 g (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 g = 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) = -0.01x² – 0.015y2 + 72x + 48y – 0.010xy – 10000
(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?
$ 122480
Transcribed Image Text: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 g (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 g = 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) = -0.01x² – 0.015y2 + 72x + 48y – 0.010xy – 10000 (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? $ 122480
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