An industry is manufacturing two types of products A and B. The profits per Kg of the two
products are Rs 30 and Rs 40 respectively. These two products require processing in three types of
machines. The following table shows the available machine hours per day and the time required on each
machine to produce one Kg of A and B. Formulate the linear programming model
| Profit/Kg | A | B | Total available
Machine hours/day |
| Machine-1 | 3 | 2 | 600 |
| Machine-2 | 3 | 5 | 800 |
| Machine-3 | 5 | 6 | 1100 |
Solution:
Decision variables
Here Products A and B are competing variables and Machines are available resources.
Let x1, x2 denotes quantity of product A, B respectively
The LP Model
The profits of the two products are Rs 30 and Rs 40 respectively. The objective of the problem is to maximize the profit Z,
Hence objective function is
Maximize Z = 30x1 + 40x2
The utilization of machine hours by products A and B should not exceed the available capacity.
This can be shown as follows
For Machine-1 : 3x1 + 2x2 ≤ 600
For Machine-2 : 3x1 + 5x2 ≤ 800
For Machine-3 : 5x1 + 6x2 ≤ 1100
There is no negative production. Hence we can write,
x1, x2 ≥ 0
Thus, the linear programming model is
Maximize Z = 30x1 + 40x2
Subject to
3x1 + 2x2 ≤ 600
3x1 + 5x2 ≤ 800
5x1 + 6x2 ≤ 1100
and x1, x2 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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