Page 85 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Figure 3.6: Graphical Representation of unbounded solution

3.4.3 Infeasibility

Infeasibility is a condition that arises when constraints are inconsistent (mutually exclusive) i.e.
no value of the variables satisfy all the constraint simultaneously. This results in infeasible
solution. If two or more constraints of a linear programming problem are mutually conflicting,
it does not have a feasible solution. Let us take a problem to illustrate infeasibility.

Example: The Reddin Hardware Ltd. is producing two products, A and B. The profit
contribution of product A is ` 5 per unit and of product B ` 4 per unit. Both the products go
through the processing and assembly departments. Product A takes two minutes in the processing
department and two minutes in the assembly department. Product B takes one minute in the
processing department and one and a half minute in the assembly department. The maximum
capacity of the processing department is 10,000 worker-minutes and of the assembly department
12,000 worker-hours. The marketing department has informed that a contract has been made
with a hardware chain store for the supply of 6,500 units of product A and that there is no other
demand for this product. There is no marketing constraint in the case of product B. What is the
optimum product mix for the company?

The linear programming mode for the Reddin Hardware is as follows:
Let
x = product A
1
x = product B
2
Maximise ‘Z’ = 5x + 4x Objective Function
1 2
2x + 1x  10,000 Processing Constraint
1 2
2x + x  12,000 Assembly Constraint
1 2
x = 6,500 Demand Constraint
1
x  0 Non-negativity Constraint
1

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