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  • Solve the following Linear Programming Problems graphically minimise and maximise z =x + 2y

8. Solve the following Linear Programming Problems graphically:

Minimise and Maximisez=x+2y 

Subject tox+2y\geq 100,2x-y\leq 0,2x+y\leq 200,x,y,\geq 0 

Show that the minimum of Z occurs at more than two points.

Answers (1)

best_answer

The region determined by constraints x+2y\geq 100,2x-y\leq 0,2x+y\leq 200,x,y,\geq 0is as follows,

               

The corner points of the feasible region are A(0,50),B(20,40),C(50,100),D(0,200)

 The value of these points at these corner points are : 

Corner points            z=x+2y  
        A(0,50)                100 Minimum

        B(20,40)

               100 Minimum
       C(50,100)               250  
        D(0,200)                400 Maximum

The minimum value of Z is 100  at all points on the line segment joining points  A(0,50) and B(20,40).

The maximum value of Z is 400 at D(0,200).

Posted by

seema garhwal

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