A company owns two flour mills A and B, which have different production capacities for high,
medium and low quality flour. The company has entered a contract to supply flour to a firm every month
with at least 8, 12 and 24 quintals of high, medium and low quality respectively. It costs the company
Rs 2000 and Rs 1500 per day to run mill A and B respectively. In one day, Mill A produces 6, 2 and 4
quintals of high, medium and low quality flour respectively, Mill B produces 2, 4 and 12 quintals of high, medium
and low quality flour respectively. Formulate the linear programming model to Minimize the cost.
Solution:
The contents of the statement of the problem can be summarized as follows
| Mill | A | B | MinRequired |
| high | 6 | 2 | 8 |
| medium | 2 | 4 | 12 |
| low | 4 | 12 | 24 |
Decision variables
Here flour mills A and B are competing variables and flour quality are available resources.
Let x1 and x2 denotes mills A and B respectively
The LP Model
Here the objective is to minimize the cost
Minimize Z = 2000x1 + 1500x2
Subject to
6x1 + 2x2 ≥ 8
2x1 + 4x2 ≥ 12
4x1 + 12x2 ≥ 24
and x1, x2 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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