A company manufactures two products X and Y. The profit contribution of X and Y are
Rs 3 and Rs 4 respectively. The products X and Y require the services of four facilities. The
capacities of the four facilities A, B, C, and D are limited and the available capacities in hours are 200
Hrs, 150 Hrs, and 100 Hrs and 80 hours respectively. Product X requires 5, 3, 5 and 8 hours of
facilities A, B, C and D respectively. Similarly the requirement of product Y is 4, 5, 5, and 4 hours
respectively on A, B, C and D.
Formulate the linear programming model to Maximize the profit.
Solution:
The contents of the statement of the problem can be summarized as follows
| Machines | X | Y | Total |
| A | 5 | 4 | 200 |
| B | 3 | 5 | 150 |
| C | 5 | 4 | 100 |
| D | 8 | 4 | 80 |
Decision variables
Here Products X and Y are competing variables and facilities A, B, C, and D are available resources.
Let x1, x2 denotes number of products X, Y respectively
The LP Model
Maximize Z = 3x1 + 4x2
subject to
5x1 + 4x2 ≤ 200
3x1 + 5x2 ≤ 150
5x1 + 4x2 ≤ 100
8x1 + 4x2 ≤ 80
and x1, x2 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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