A manufacturer produces three models (I, II, and II) of a certain product using raw materials A and B. The labor time per unit model of I is twice that of Il and three times that of III. The entire labor force of the factory can produce the equivalent of 1500 units of Model I. Market requirements specify the ratios 3:2:5 for the production of the three respective models and minimum demand levels should be satisfied. Requirement Raw Material II Availability A 2 3 4000 B 4 2 7 6000 Minimum demand 200 200 150 Price per unit 30 20 50

Practical Management Science
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Author:WINSTON, Wayne L.
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A manufacturer produces three models (I, II, and III) of a certain product using raw materials A and B. The labor
time per unit model of I is twice that of Il and three times that of III. The entire labor force of the factory can
produce the equivalent of 1500 units of Model I. Market requirements specify the ratios 3:2:5 for the
production of the three respective models and minimum demand levels should be satisfied.
Requirement
Raw Material
II
Availability
A
2
3
5
4000
В
4
2
7
6000
Minimum demand
200
200
150
Price per unit
30
20
50
The objective is to maximize the total revenue.
a. Formulate a linear programming model for this problem.
b. Discuss your findings in the context of assumptions of linear programming.
Transcribed Image Text:A manufacturer produces three models (I, II, and III) of a certain product using raw materials A and B. The labor time per unit model of I is twice that of Il and three times that of III. The entire labor force of the factory can produce the equivalent of 1500 units of Model I. Market requirements specify the ratios 3:2:5 for the production of the three respective models and minimum demand levels should be satisfied. Requirement Raw Material II Availability A 2 3 5 4000 В 4 2 7 6000 Minimum demand 200 200 150 Price per unit 30 20 50 The objective is to maximize the total revenue. a. Formulate a linear programming model for this problem. b. Discuss your findings in the context of assumptions of linear programming.
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