Find the maximum and minimum values, Operation Research

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Problems based on solution of a given LPP when it has multiple optimal solution:

1. Find the maximum and minimum values of 5x+2y, subject to the constraints

-2x-3y ≤ -6

x-2y ≤ 2

6x + 4y ≤ 24

-3x + 2y ≤ 3

X, y ≥ 0

script

solution

1. Let z is equal to

Let us draw the lines - 2x-3y = -6, X - 2y =2

6x+ 4y = 24

2. using suitable points on the graph.

3. Now shade the region of intersection of the 3 lines.

4. The shaded region ABCD represents the region of feasible region

5. The Vertices of feasible region are

6. Now let us find the maximum and minimum values by using these points

7. For the corner point A(18/7,2/7)

8. For the corner point B(7/2,3/4)

9. For the corner point C(3/2,15/4)

10. For the corner point D(3/13,24/13)

11. We find the maximum value occurs at vertex B, minimum value at vertex D

Maximum value

Minimum value

Z = 5x + 2y

2x + 3y = 6

X - 2y =2

6x+ 4y = 24

- 3x + 2y = 3

A ( 18\7,2\7) B(7\2,3\4) C(3\2,15\4) D(3\13,24\13)

5(18/7)+2(2/7)= 94/7

5(7/2)+2(3/4)=76/4

5(3/2)+2(15/4)=60/4

5(3/13)+2(24/13)=63/13

63\13

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