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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 a (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, v) - What is the maximum weekly profit?

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 a (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, v) - What is the maximum weekly profit?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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) = (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? (х, у) 3D What is the maximum weekly profit? $
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) = (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? (х, у) 3D What is the maximum weekly profit? $
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