Page 75 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Therefore, ‘Z’ = C X
B B
= (2 × 0.9) + (0 × 1.87) + (1.5 × 1.19) + (5 × 0.009)
= 1.8 + 0 + 1.79 + 0.045
= 3.64

Did u know? Big 'M' Method is also known as 'Charnes' 'M' Technique.

!
Caution If the objective function z is to be minimized, then a very large positive price
(called penalty) is assigned to each artificial variable. Similarly, if Z is to be maximized,
then a very large negative price (also called penalty) is assigned to each of these variables.
The only visible difference between these two penalty is that the one will be designated
by -M for a maximization problem and +M for a minimization problem, where M>0.

Self Assessment

6. Solve the following LPP using the Big M method.
Maximise ‘Z’ = 40x + 60x [Subject to constraints]
1 2
2x + x  70
1 2
x + x  40
1 2
x + x  40
1 2
x + 3x  90
1 2
Where, x , x  0
1 2
7. Solve the following LPP using the Big M method.
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
Where, x , x  0
1 2
3.3 Unconstrained Variables

Sensitivity analysis involves 'what if?' questions. In the real world, the situation is constantly
changing like change in raw material prices, decrease in machinery availability, increase in
profit on one product, and so on. It is important to decision makers for find out how these
changes affect the optimal solution. Sensitivity analysis can be used to provide information and
to determine solution with these changes.
Sensitivity analysis deals with making individual changes in the coefficient of the objective
function and the right hand sides of the constraints. It is the study of how changes in the coefficient
of a linear programming problem affect the optimal solution.

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