GATE ME 2015 Set 3 — Question 61
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Industrial Engineering → Operations Research → LP (Graphical & Simplex)
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Question
For the linear programming problem:
Maximize
Subject to
The above problem has
Maximize
Subject to
The above problem has
Correct answer
(A) unbounded solution
Solution
The constraints for the linear programming problem are:
1)
2)
3) In the first quadrant (), as increases towards infinity, we can always find a value for (for example, ) that satisfies both constraints. For , the constraints become and , both of which are satisfied for all .
The objective function is . As and , . Since the objective function can increase without bound within the feasible region, the problem has an unbounded solution.
1)
2)
3) In the first quadrant (), as increases towards infinity, we can always find a value for (for example, ) that satisfies both constraints. For , the constraints become and , both of which are satisfied for all .
The objective function is . As and , . Since the objective function can increase without bound within the feasible region, the problem has an unbounded solution.
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