A firm manufactures two types of Product A and B and sells them a profit of Rs. 12.00 on type A and Rs 13.00 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing on G and two minutes on H; Type B requires one minute on G and one minute on H. The machine G is available for not more than 6 while Machine H is available for 10 minutes during any working day. Formulate the problem as a linear programming problem. DATA SUMMARY CHART Variable Machine G Machine H Profit per unit Rs. Minutes Minutes Product A 1 2 12 Product B 1 1 13 Resource 10 6.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Solve the optimization problem using linear programming. Find the optimal solution with graph.

Problem 1
A firm manufactures two types of Product A and B and sells them a profit of Rs.
12.00 on type A and Rs 13.00 on type B. Each product is processed on two
machines G and H. Type A requires one minute of processing on G and two
minutes on H; Type B requires one minute on G and one minute on H. The
machine G is available for not more than 6 while Machine H is available for 10
minutes during any working day. Formulate the problem as a linear programming
problem.
DATA SUMMARY CHART
Variable
Machine G
Machine H
Profit per unit Rs.
Minutes
Minutes
Product A
1
12
Product B
1
1
13
Resource
6.
10
A. Decision Variables
Product A = X1
Product B = X2
B. Maximize (z) = 12X1 + 13X2
C. Constraint
Machine G minutes = 1X1 + 1X2 s6
Machine H minutes = 2X1 + 1X2 s 10
2.
Transcribed Image Text:Problem 1 A firm manufactures two types of Product A and B and sells them a profit of Rs. 12.00 on type A and Rs 13.00 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing on G and two minutes on H; Type B requires one minute on G and one minute on H. The machine G is available for not more than 6 while Machine H is available for 10 minutes during any working day. Formulate the problem as a linear programming problem. DATA SUMMARY CHART Variable Machine G Machine H Profit per unit Rs. Minutes Minutes Product A 1 12 Product B 1 1 13 Resource 6. 10 A. Decision Variables Product A = X1 Product B = X2 B. Maximize (z) = 12X1 + 13X2 C. Constraint Machine G minutes = 1X1 + 1X2 s6 Machine H minutes = 2X1 + 1X2 s 10 2.
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