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  • Solve the following Linear Programming Problems graphically Z = x + 2y.

6. Solve the following Linear Programming Problems graphically:

Minimise Z = x + 2y

Subject to 2x+y\geq 3,x+2y\geq 6,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 2x+y\geq 3,x+2y\geq 6,x,y\geq 0.is as follows,

               

The corner points of the feasible region are A(6,0),B(0,3)

 The value of these points at these corner points are : 

Corner points            Z = x + 2y
        A(6,0)                6

   B(0,3)

               6

Value of Z is the same at both points.A(6,0),B(0,3)

If we take any other point like (2,2) on line Z = x + 2y , then Z=6.

Thus the minimum value of Z occurs at more than 2 points .

Therefore, the value of Z is minimum at every point on the line  Z = x + 2y.

Posted by

seema garhwal

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