x-2yge0,2x-yle-2,xge0,yge0

Consider the linear inequalities 2x+3yle6, 2x+y le 4, x ge0, y ge0 (i) Mark the feasible region. (ii) Maximise the function Z=4x+5y subject to the given constraints.

Determine the region in the plane determined by the inequalities. 2x + 3y le 6, x + 4y le 4, x ge 0 , y ge 0 .

2x+3yle35,yge2,xge5

Solve the following linear programming problem graphically: Minimise Z=200x+500y ……………1 subject to the constraints: x+2yge10 ……………2 3x+4yle24 ……………3 xge0,yge0 …………..4

The corner points of the feasible region determined by the following sytem of linear inequalities: 2x+yle10, x+3yle15, x, yge0 are (0,0),(5,0),(3,4) and (0,5). Let Z=px+qy where p,qge0 . Condition on p and q so that the maximum of Z occurs at both (3,4) and (0,5) is

Determine graphically the minimum value of the objective function Z=-50x+20y ……………1 subject to the constraints: 2x-yge-5 …………..2 3x+yge3 ………….3 2x-3yle12 ……………..4 xge0, yge0 …………5

Solve the following linear programming problem graphically: Maximise Z=4x+y ………….1 subject to the constraints: x+yle50 ……………2 3x+yle90 …………..3 xge0, yge0 …………..4

If g(x)=max(y^(2)-xy)(0le yle1) , then the minimum value of g(x) (for real x) is

f(x)={{:(x^(2)", "xle2),(8-2x", "2ltxlt4),(4", "xge4):}