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The feasible region of the LPP Min z = 3x + 2y subject to constraints 2x + y ≥ 6, x − y ≥ 0, x ≥ 0, y ≥ 0 is given below:

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The feasible region of the LPP

Min z = 3x + 2y

subject to constraints

2x + y ≥ 6, x − y ≥ 0, x ≥ 0, y ≥ 0 is given below:

Determine the optimal solution. Justify your answer.

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1 Answer

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Corner Point Z = 3x + 2y
P (2, 2) 10
Q (3, 0) 9

The smallest value of Z is 9. Since the feasible region is unbounded, we draw the graph of 3x + 2y < 9. The resulting open half plane has points common with feasible region, therefore Z = 9 is not the minimum value of Z. Hence the optimal solution does not exist.

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