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  • Solve the following Linear Programming Problems graphically Z = 5x + 10y

 7. Solve the following Linear Programming Problems graphically:

Minimise and Maximise z=5x+10y

Subject to x+2y\leq 120,x+y\geq 60,x-2y\geq 0,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\leq 120,x+y\geq 60,x-2y\geq 0,x,y\geq 0 is as follows,

               

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

 The value of these points at these corner points are : 

Corner points            z=5x+10y  
        A(40,20)                400  

        B(60,30)

                600 Maximum
       C(60,0)                300

Minimum
        D(120,0)                600 maximum

The minimum value of Z is 300  at  C(60,0)  and maximum value is 600 at all points joing line segment  B(60,30) and D(120,0)

Posted by

seema garhwal

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