A company manufactures two products, X and Y by using three machines A, B, and C.
Machine A, B and C has 4 hours, 24 hours and 35 hours of capacity respectively, available during the coming week.
One unit of product X requires 1 hour, 3 hour and 10 hours of machine A, B and C respectively. Similarly
one unit of product Y requires 1 hour, 8 hour and 7 hours of machine A, B and C respectively.
Profit of product X is Rs 5 per product and that of Y is Rs 7 per product.
Formulate the linear programming model
Solution:
The contents of the statement of the problem can be summarized as follows
| Machines | X | Y | hours of capacity |
| A | 1 | 1 | 4 |
| B | 3 | 8 | 24 |
| C | 10 | 7 | 35 |
Decision variables
Here Products X and Y are competing variables and Machine A,B,C are available resources.
Let x1, x2 denotes number of products X, Y respectively
The LP Model
Maximize Z = 5x1 + 7x2
subject to
x1 + x2 ≤ 4
3x1 + 8x2 ≤ 24
10x1 + 7x2 ≤ 35
and x1, x2 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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