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A factory produces four products, D, C, B, A, using two machines Mand M. The time taken and the cost of producing one unit on each of the two machines and the available time to operate for each machine and the selling price per unit for each product are shown in the table below: machines Time per unit ( hours/unit)| Cost Availability hours A B D (I.D./hour) M1 M2 Sales price (1.D./unit) 3 4 10 500 3 2 2 15 380 65 70 55 45 Note that the total cost of producing one unit depends directly on the operating time of the machine. It is required to formulate a mathematical model for the linear programming of the above problem to achieve: a) The lowest total cost. And b) the highest total net profit.

A factory produces four products, D, C, B, A, using two machines Mand M. The time taken and the cost of producing one unit on each of the two machines and the available time to operate for each machine and the selling price per unit for each product are shown in the table below: machines Time per unit ( hours/unit)| Cost Availability hours A B D (I.D./hour) M1 M2 Sales price (1.D./unit) 3 4 10 500 3 2 2 15 380 65 70 55 45 Note that the total cost of producing one unit depends directly on the operating time of the machine. It is required to formulate a mathematical model for the linear programming of the above problem to achieve: a) The lowest total cost. And b) the highest total net profit.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 56P
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A factory produces four products, D, C, B, A, using two machines Mand M. The time taken and the cost of producing one unit on each of the two machines and the available time to operate for each machine and the selling price per unit for each product are shown in the table below: machines Time per unit ( hours/unit) Cost Availability hours A C (I.D./hour) MI M2 Sales price (1.D./unit) 10 500 3 15 380 65 70 55 45 - Note that the total cost of producing one unit depends directly on the operating time of the machine. It is required to formulate a mathematical model for the linear programming of the above problem to achieve: a) The lowest total cost. And b) the highest total net profit.
Transcribed Image Text:A factory produces four products, D, C, B, A, using two machines Mand M. The time taken and the cost of producing one unit on each of the two machines and the available time to operate for each machine and the selling price per unit for each product are shown in the table below: machines Time per unit ( hours/unit) Cost Availability hours A C (I.D./hour) MI M2 Sales price (1.D./unit) 10 500 3 15 380 65 70 55 45 - Note that the total cost of producing one unit depends directly on the operating time of the machine. It is required to formulate a mathematical model for the linear programming of the above problem to achieve: a) The lowest total cost. And b) the highest total net profit.
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