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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	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.