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2. A firm makes two products X and Y, and has a total production capacity of 9 tonnes per day. Both X and Y require the same production capacity. The firm has a permanent contract to supply at least 2 tonnes of X and at least 3 tonnes of Y per day to another company. Each tonne of X requires 20 machine hours of production time and each tonne of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. All of the firm's output can be sold. The profit made is GHs 80 per tonne of X and GHs 120 per tonne of Y. a) Formulate this problem as a Linear programming model. b) Use the graphical method to determine the production schedule that yields the maximum profit.

2. A firm makes two products X and Y, and has a total production capacity of 9 tonnes per day. Both X and Y require the same production capacity. The firm has a permanent contract to supply at least 2 tonnes of X and at least 3 tonnes of Y per day to another company. Each tonne of X requires 20 machine hours of production time and each tonne of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. All of the firm's output can be sold. The profit made is GHs 80 per tonne of X and GHs 120 per tonne of Y. a) Formulate this problem as a Linear programming model. b) Use the graphical method to determine the production schedule that yields the maximum 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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2. A firm makes two products X and Y, and has a total production capacity of 9 tonnes per day. Both X and Y require the same production capacity. The firm has a permanent contract to supply at least 2 tonnes of X and at least 3 tonnes of Y per day to another company. Each tonne of X requires 20 machine hours of production time and each tonne of Y requires 50 machine hours of production tỉme. The daily maximum possible number of machine hours is 360. All of the firm's output can be sold. The profit made is GHs 80 per tonne of X and GHs 120 per tonne of Y. a) Formulate this problem as a Linear programming model. b) Use the graphical method to determine the production schedule that yields the maximum profit.
Transcribed Image Text:2. A firm makes two products X and Y, and has a total production capacity of 9 tonnes per day. Both X and Y require the same production capacity. The firm has a permanent contract to supply at least 2 tonnes of X and at least 3 tonnes of Y per day to another company. Each tonne of X requires 20 machine hours of production time and each tonne of Y requires 50 machine hours of production tỉme. The daily maximum possible number of machine hours is 360. All of the firm's output can be sold. The profit made is GHs 80 per tonne of X and GHs 120 per tonne of Y. a) Formulate this problem as a Linear programming model. b) Use the graphical method to determine the production schedule that yields the maximum profit.
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