Question

Solve the following LPP graphically:

Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0

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Answer 1

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The shaded region (OAB) in the Fig. 12.3 is the feasible region determined by the system of constraints x ≥ 0, y ≥ 0 and x + y ≤ 4.

The feasible region OAB is bounded, so, maximum value will occur at a corner point of the feasible region.

Corner Points are O(0, 0), A (4, 0) and B (0, 4).

Evaluate Z at each of these corner point.

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Hence, the maximum value of Z is 12 at the point (0, 4)

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Answer 2

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•The shaded region (OAB) in the Fig. 12.3 is the feasible region determined by the system of constraints x ≥ 0, y ≥ 0 and x + y ≤ 4.

•The feasible region OAB is bounded, so, maximum value will occur at a corner point of the feasible region.

•Corner Points are O(0, 0), A (4, 0) and B (0, 4).

Evaluate Z at each of these corner point.

•Hence, the maximum value of Z is 12 at the point (0, 4)

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