Solve the following linear programming problem graphically:
Minimise Z = 50x + 25y
subject to the constraints:
x + 2y ≥ 10
3x + 4y ≤ 24
x ≥ 0, y ≥ 0

125

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150

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275

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400

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Solution

The correct option is A 125
The shaded region in Figure is the feasible region ABC determined by the
system of constraints, which is bounded. The coordinates of corner points

Corner Point Corresponding Value of Z

(0, 6) 150

(4, 3) 275

(0, 5) 125

A, B and C are (0,5), (4,3) and (0,6) respectively. Now we evaluate
Z = 50x+25y
at these points.
Hence, minimum value of Z is 125 attained at the point (0, 5)

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