The minimum value of the objective function z=-50x+20y subject to constraits `2x-yge-5, 32x+yge3`
`2x-3y le 12` and `x ge0,yge0`

3x+2y le 12, x ge 1, y ge 2

Maximise Z=-x+2y , subject to the constraint, xge3, x+yge5, yge0

Maximise Z=3x+4y Subject to the constraints x+yle4, xge0, yge0

Minimise Z=3x+2y subject to the constraints, x+yge8 ………..1 3x+5yle15 …………2 xge0, yge0 ………..3

Solve the follwing LPP by the graphical method Min Z= 32x+y Subject to the constraints 2x+y ge 14 x-y ge 4 and x ge 0, y ge 0

Solve the following linear programming problem by graphical method and find the maximum value of Z. (Graph sheet is not required): Z = x+y Subject to the constraints , 5x+10yle50,x+yge1,yle4,x,yge0 .

Represent geometrically the following LPP Minimize Z= 3x+2y Subject to the constraits 5x+y ge 10 x+yge6 x+4yge12 and x ge 0 ,y ge 0 find out the exterme points of the convex set of feasible solution and hence find out the minimum value of the objective function

The maximum value of Z=3x+4y subject to the constraints x+y le 40, x+2y le 60, x ge 0 and y ge 0 is -