Routing 1 uses drying press A, and routing 2 uses drying press B. Both routings require the same mixing to blend chemicals for the dye before drying. The following table shows the time requirements and capacities of these processes: Routing 1 Process Mixing Dryer A Dryer B 0 8 Each kilogram of dye processed on routing 1 uses 20 titers of chemicals, whereas each kilogram of dye processed on routing 2 uses only 15 liters. The difference results from differing yield rates of the drying presses. Consequently, the profit per kilogram processed on routing 1 is $50 and on routing 2 Is $65. A total of 450 liters of input chemicals is available. 1. Write the constraints and objective function to maximize profits. 2. Use the graphic method of linear programming to find the optimal solution. 2 Time requirements (hr/kg) Routing 2 6 Capacity (hr) 2 0 54 120 180

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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A manufacturer of textile dyes can use two different processing routings for a particular type of dye.
Routing 1 uses drying press A, and routing 2 uses drying press B. Both routings require the same mixing v
to blend chemicals for the dye before drying. The following table shows the time requirements and
capacities of these processes:
Routing 1
Process
Mixing
Dryer A
0
Dryer B
8
Each kilogram of dye processed on routing 1 uses 20 titers of chemicals, whereas each kilogram of dye
processed on routing 2 uses only 15 liters. The difference results from differing yield rates of the drying
presses. Consequently, the profit per kilogram processed on routing 1 is $50 and on routing 2 Is $65. A
total of 450 liters of input chemicals is available.
1. Write the constraints and objective function to maximize profits.
2. Use the graphic method of linear programming to find the optimal solution.
2
Time requirements (hr/kg)
Routing 2
6
0
Capacity (hr)
2
54
120
180
Transcribed Image Text:A manufacturer of textile dyes can use two different processing routings for a particular type of dye. Routing 1 uses drying press A, and routing 2 uses drying press B. Both routings require the same mixing v to blend chemicals for the dye before drying. The following table shows the time requirements and capacities of these processes: Routing 1 Process Mixing Dryer A 0 Dryer B 8 Each kilogram of dye processed on routing 1 uses 20 titers of chemicals, whereas each kilogram of dye processed on routing 2 uses only 15 liters. The difference results from differing yield rates of the drying presses. Consequently, the profit per kilogram processed on routing 1 is $50 and on routing 2 Is $65. A total of 450 liters of input chemicals is available. 1. Write the constraints and objective function to maximize profits. 2. Use the graphic method of linear programming to find the optimal solution. 2 Time requirements (hr/kg) Routing 2 6 0 Capacity (hr) 2 54 120 180
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