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in Linear Programming by (49.9k points)
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Maximize Z = 3x + 5y, subject to the constraints

x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0 and y ≥ 0

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Best answer

It is given that

Z = 3x + 5y, subject to the constraints

x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0 and y ≥ 0

Draw the line x + 2y = 2000, x + y = 1500 and y = 600 and shaded region which is satisfied by above inequalities

We know that the feasible region is bounded

O (0, 0), A (1000, 500), B (800, 600), C (0, 600) and D (1500, 0) are the corner points

So the value of Z at O (0, 0)

Z = 0

Value of Z at A (1000, 500)

Z = 5500

Value of Z at B (800, 600)

Z = 5400

Value of Z at C (0, 600)

Z = 3000

Value of Z at D (1500, 0)

Z = 4500

Hence, the maximum value of Z is 5500 which occurs at A (1000, 500).

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