Page 47 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 5: Substitute the co-ordinates of the corner points to the objective function.
Maximise ‘Z’ = 7x + 3x
1 2
At ‘A’, Z = 7(2.5) + 3(0.17) = 18.01
At ‘B’, Z = 7(2.5) + 3(1.5) = 22

At ‘C’, Z = 7(0) + 3(1.5) = 4.5
At ‘D’, Z = 7(0) + 3(1) = 3

Inference

Hence, the company can get maximum profit by producing 2.5 units of product A and 3 units of
product B.

Example:
Maximise ‘Z’ = 5x + 3x (Subject to constraints)
1 2
x + x  6
1 2
2x + 3x  3
1 2
x  3
1
x  3
2
x , x  0 (Non-negativity constraints)
1 2
Solution:
Step 1: Find the divisible of the equalities.

Equation x1 x2
x 1 + x 2 = 6 6 6
2x1 + 3x2 = 3 1.5 1
x 1 = 3 3 0
x2 = 3 0 3

Step 2: Fix up the graphic scale
Maximum points = 6
Minimum points = 1
1 cm. = 1 point
Step 3: Graph the data

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