Kpogas produces chairs and tables. Using economic forecast for the next month, Kpogas’ marketing manager has judged that during that period, it will be possible to sell as many chairs or tables as the company can produce. Management must now recommend a production target for next month. That is, how many chairs and tables should be produced if Kpogas’ management wishes to maximize next month’s profit contribution? Making this decision requires a consideration of the following key factors: ● Kpogas’s unit contribution margin is GH¢ 5,000 on each chair that is sold and GH¢ 4,000 on each table that is sold. ● Each product is put through Kpogas’s machining operations in both department A and department B. For next month’s production, the two departments have 150 and 160 hours available time, respectively. Each chair produced uses 10 hours of machining in department A and 20 hours of machining in department B, whereas each table produced uses 15 hours of machining in department A and 10 hours of machining in department B. 9 Major Topic 12 Markov: Score Question 5 ● In order for management to honour an agreement with the union, the total labour hours used in the next month’s testing of finished products cannot fall more than 10% below an arbitrated goal of 150 hours. Since 10% of 150 is 15, the total hours devoted to testing cannot fall below 135. The testing is performed in the third department and has nothing to do with department A and B. Each chair is given 30 hours of testing and each table is given 10. ● To maintain current market position, management has decided that it is necessary to build at least one chair for every three tables produced. ● A major dealer has ordered a total of at least five chairs and tables (in any combination) for next month, and so at least that number must be produced. (i) Define the decision variables for this problem (ii) Formulate a linear programming model for this problem.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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Kpogas produces chairs and tables. Using economic forecast for the next month, Kpogas’ marketing manager has judged that during that period, it will be possible to sell as many chairs or tables as the company can produce. Management must now recommend a production target for next month. That is, how many chairs and tables should be produced if Kpogas’ management wishes to maximize next month’s profit contribution? Making this decision requires a consideration of the following key factors: ● Kpogas’s unit contribution margin is GH¢ 5,000 on each chair that is sold and GH¢ 4,000 on each table that is sold. ● Each product is put through Kpogas’s machining operations in both department A and department B. For next month’s production, the two departments have 150 and 160 hours available time, respectively. Each chair produced uses 10 hours of machining in department A and 20 hours of machining in department B, whereas each table produced uses 15 hours of machining in department A and 10 hours of machining in department B. 9 Major Topic 12 Markov: Score Question 5 ● In order for management to honour an agreement with the union, the total labour hours used in the next month’s testing of finished products cannot fall more than 10% below an arbitrated goal of 150 hours. Since 10% of 150 is 15, the total hours devoted to testing cannot fall below 135. The testing is performed in the third department and has nothing to do with department A and B. Each chair is given 30 hours of testing and each table is given 10. ● To maintain current market position, management has decided that it is necessary to build at least one chair for every three tables produced. ● A major dealer has ordered a total of at least five chairs and tables (in any combination) for next month, and so at least that number must be produced. (i) Define the decision variables for this problem (ii) Formulate a linear programming model for this problem.

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