A factory manufactures two products A and B on three machines X, Y, and Z. Product
A requires 10 hours of machine X and 5 hours of machine Y 1 hour of machine Z. The requirement
of product B is 6 hours, 10 hours and 2 hours of machine X, Y and Z respectively. The profit contribution
of products A and B are Rs 23 per unit and Rs 32 per unit respectively. In the coming planning
period the available capacity of machines X, Y and Z are 2500 hours, 2000 hours and 500 hours
respectively. Find the optimal product mix for maximizing the profit.
Solution:
The contents of the statement of the problem can be summarized as follows
| Machines | A | B | Capacity hours |
| X | 10 | 6 | 2500 |
| Y | 5 | 10 | 2000 |
| Z | 1 | 2 | 500 |
| Profit/unit Rs | 23 | 32 | |
Decision variables
Here Products A and B are competing variables and Machine X,Y,Z are available resources.
Let x1, x2 denotes units of products A, B respectively
The LP Model
Maximize Z = 23x1 + 32x2
subject to
10x1 + 6x2 ≤ 2500
5x1 + 10x2 ≤ 2000
x1 + 2x2 ≤ 500
and x1, x2 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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