Page 43 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 40 + 50x = 360
2
50x = 320
2
Therefore x = 6.4
2
Steps 5: Substitute the values of co-ordinates of the corner points to the objective function.
Maximise ‘Z’ = 80x + 120x
1 2
At ‘A’, Z = 80(2) + 120(3) = 520
At ‘B’, Z = 80(6) + 120(3) = 840
At ‘C’, Z = 80(3) + 120(6) = 960

At ‘D’ Z = 80(2) + 120(6.4) = 928

Inference

The company has to produce 3 tonnes of product x and 6 tonnes of product y in order to maximize
the profit.

Example:
Maximise ‘Z’ = 40x + 60x (Subject to constraints)
1 2
2x + x  70
1 2
x + x  40
1 2
x + 3x  90
1 2
x , x  0 (Non-negativity constraints)
1 2
Solution:
Step 1: Find the divisibles of the equalities.

Equation x1 X2
2x 1 + x 2 = 70 35 70
x1 + x2 = 40 40 40
x 1 + 3x 2 = 90 90 30

Step 2: Fix up the graphic scale
Maximum points = 90
Minimum points = 30
1 cm. = 10 points

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