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A company has two CNC machines and it produces four different products. The processing times of the products differ depending on which machine they are processed. Related information about the products is shown in the following table. Processing Time (minutes) Machine A Product Machine B Profit 1 10 27 100 12 13 19 120 33 170 4 8 23 80 Each product can be produced on either machine A or machine B. The quantity ofproduct 2 to be produced is related to the quantity of product 3 to be produced. The quantity of product 2 should be at least two times greater than the quantity of product 3. The breakdowns occur from time to time and hence machine A is out of order 6% of the time and machine B 8% of the time. Assuming a working week 35 hours long formulate the problem of how to manufacture these products as a linear program. Requirements Define the decision variables clearly. b. Add a short explanation for each constraint.

A company has two CNC machines and it produces four different products. The processing times of the products differ depending on which machine they are processed. Related information about the products is shown in the following table. Processing Time (minutes) Machine A Product Machine B Profit 1 10 27 100 12 13 19 120 33 170 4 8 23 80 Each product can be produced on either machine A or machine B. The quantity ofproduct 2 to be produced is related to the quantity of product 3 to be produced. The quantity of product 2 should be at least two times greater than the quantity of product 3. The breakdowns occur from time to time and hence machine A is out of order 6% of the time and machine B 8% of the time. Assuming a working week 35 hours long formulate the problem of how to manufacture these products as a linear program. Requirements Define the decision variables clearly. b. Add a short explanation for each constraint.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 58P
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A company has two CNC machines and it produces four different products. The processing times of the products differ depending on which machine they are processed. Related information about the products is shown in the following table. Processing Time (minutes) Product Machine A Machine B Profit 1 10 27 100 2 12 19 120 13 33 170 4 23 80 Each product can be produced on either machine A or machine B. The quantity of product 2 to be produced is related to the quantity of product 3 to be produced. The quantity of product 2 should be at least two times greater than the quantity of product 3. The breakdowns occur from time to time and hence machine A is out of order 6% of the time and machine B 8% of the time. Assuming a working week 35 hours long formulate the problem of how to manufacture these products as a linear program. Requirements a. Define the decision variables clearly. b. Add a short explanation for each constraint.
Transcribed Image Text:A company has two CNC machines and it produces four different products. The processing times of the products differ depending on which machine they are processed. Related information about the products is shown in the following table. Processing Time (minutes) Product Machine A Machine B Profit 1 10 27 100 2 12 19 120 13 33 170 4 23 80 Each product can be produced on either machine A or machine B. The quantity of product 2 to be produced is related to the quantity of product 3 to be produced. The quantity of product 2 should be at least two times greater than the quantity of product 3. The breakdowns occur from time to time and hence machine A is out of order 6% of the time and machine B 8% of the time. Assuming a working week 35 hours long formulate the problem of how to manufacture these products as a linear program. Requirements a. Define the decision variables clearly. b. Add a short explanation for each constraint.
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