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Solve the Following L.P.P. Graphically: Minimise Z = 5x + 10y Subject to X + 2y ≤ 120 Constraints X + Y - Mathematics

Solve the following L.P.P. graphically: 

Minimise Z = 5x + 10y

Subject to x + 2y ≤ 120

Constraints x + y ≥ 60

x – 2y ≥ 0 and x, y ≥ 0

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Solution

The feasible region determined by the constraints, x + 2y ≤ 120, x + y ≥ 60, x − 2y ≥ 0, x ≥ 0, and y ≥ 0, is as follows.

The corner points of the feasible region are A (60, 0), B (120, 0), C (60, 30), and D (40, 20)

The values of Z at these corner points are as follows.

Corner point Z = 5x + 10y  
A(60, 0) 300 →Minimum
B(120, 0) 600 →Maximum
C(60, 30) 600 →Maximum
D(40, 20) 400  

The minimum value of Z is 300 at (60, 0).

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