A factory works 8 hours a day, producing three products namely A, B and C. each of these products is processed in three different operations namely 1, 2 and 3. The processing times in minutes for each of these products in each of the operations are given below along with utilization of the processes and the cost and price in kwachas for each of these three products which have unlimited demand. Product Processing time (mins) in operation Cost/unit Price/unit (K) (K) 1 2 3 A 4 3 1 10 16 B 2 1 4 8 12 C 3 4 5 5 10 Utilisation 80% 70% 90% i. Formulate a linear programming model for this problem. ii. Determine the optimal product mix using the simplex method. Give the interpretations for the values obtained in the final simplex table
A factory works 8 hours a day, producing three products namely A, B and C. each of these products is processed in three different operations namely 1, 2 and 3. The processing times in minutes for each of these products in each of the operations are given below along with utilization of the processes and the cost and price in kwachas for each of these three products which have unlimited demand. Product Processing time (mins) in operation Cost/unit Price/unit (K) (K) 1 2 3 A 4 3 1 10 16 B 2 1 4 8 12 C 3 4 5 5 10 Utilisation 80% 70% 90% i. Formulate a linear programming model for this problem. ii. Determine the optimal product mix using the simplex method. Give the interpretations for the values obtained in the final simplex table
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 111P
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Question
- A factory works 8 hours a day, producing three products namely A, B and C. each of these products is processed in three different operations namely 1, 2 and 3. The processing times in minutes for each of these products in each of the operations are given below along with utilization of the processes and the cost and price in kwachas for each of these three products which have unlimited demand.
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Product |
Processing time (mins) in operation |
Cost/unit |
Price/unit |
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(K) |
(K) |
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1 |
2 |
3 |
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A |
4 |
3 |
1 |
10 |
16 |
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B |
2 |
1 |
4 |
8 |
12 |
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C |
3 |
4 |
5 |
5 |
10 |
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Utilisation |
80% |
70% |
90% |
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i. |
Formulate a linear programming model for this problem. |
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ii. |
Determine the optimal product mix using the simplex method. |
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- Give the interpretations for the values obtained in the final simplex table
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