An organization has three machine shops A, B and C and it produces three product X, Y and Z
using these three machine shops. Each product involves the operation of the machine shops. The time
available at the machine shops A, B and C are 100, 72 and 80 hours respectively. The profit per unit of
product X, Y and Z is $22, $6 and $2 respectively. The following table shows the time required for each operation for
unit amount of each product.
| Products | A | B | C |
| X | 10 | 7 | 2 |
| Y | 2 | 3 | 4 |
| Z | 1 | 2 | 1 |
| Available Hours | 100 | 72 | 80 |
Formulate the linear programming model
Solution:
Decision variables
Here Products X,Y and Z are competing variables and Machine A,B,C are available resources.
Let x1, x2 and x3 denotes number of unit of product X, Y and Z respectively
The LP Model
Maximize Z = 22x1 + 6x2 + 2x3
Subject to
10x1 + 2x2 + x3 ≤ 100
7x1 + 3x2 + 2x3 ≤ 72
2x1 + 4x2 + x3 ≤ 80
and x1, x2, x3 ≥ 0
This material is intended as a summary. Use your textbook for detail explanation.
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