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
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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe28a910-179b-480b-84d6-eb6426309f48%2F6da6726b-4292-4afc-9eec-8e8e01867b7e%2Fi8bin7n_processed.jpeg&w=3840&q=75)
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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