Solve the following linear programming problem graphically : Minimise Z=200x+500y...(1) subject to the constraints: x+2y≥10...(2) 3x+4y≤24...(3) x≥0,y≥0...(4).
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Solution
The shaded region in Fig is the feasible region ABC determined by the system of constraints (2) to (4), which is bounded. The coordinates of corner points
Corner Point
Corresponding value of Z
(0,5)
2500
(4,3)
2300←Minimum
(0,6)
3000
A,B and C are (0,5),(4,3) and (0,6) respectively. Now we evaluate Z=200x+500y at these points.
Hence, minimum value of Z is 2300 attained at the point (4,3).