The Wearever Carpet Company manufactures two brands of carpet-shag and sculptured–in 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order: (1) Do not underutilize production capacity, which is 480 hours. (2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2.

The Wearever Carpet Company manufactures two brands of carpet-shag and sculptured–in 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order: (1) Do not underutilize production capacity, which is 480 hours. (2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2.

Name: Goal Programming The Wearever Carpet Company manufactures two brands o
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Description: Goal Programming The Wearever Carpet Company manufactures two brands of carpet–shag and sculptured–in100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lotof sculptured carpet. The company has the followin

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit?
The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 750 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,500 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients: homeless: profit: