Maximise `Z=-x+2y`, subject to the constrains.
`x ge 3, x+y ge 5,x+2y ge 6, y ge 0`.

x ge 3, y ge 2

2x+y ge 6

Maximise Z=3x+4y subject to the constraints x+y le, 4, x ge 0, y ge 0

Minimise and maximise Z=3x+9y subject to the constraints. x+3y le 60 x+y ge 10 x le y x ge 0, y ge 0

Minimise Z=3x+2y Subject to the constraints x+yge8 3x+5y le 15 x ge0, y ge0

(i) Draw the graph of 5x+4y=40,x=4,y=5 (ii) Solve the following LPP graphically maximise Z=3x+5y Subject to the conditions 5x+4y le 40, x le 4, y le 5, x,y ge0

Solve the following linear programming problem graphically. Minimize Z=200 x+500 y subject to the constraints: x+2y ge10 3x+4y le 24 x ge0, y, ge0

x-2y le 3, 3x+4y ge 12, x ge 0, y ge 1

2x+y ge 4, x +y le 3, 2x-3y ge6

2x+y ge 8, x+2y ge 10