Maximise and minimize `Z=12x+18y` subject to the constraints
`x+y le 10 , x -y le 0 , x+2yge 10 , x,y ge 0`

Maximize and minimize Z = x + 2y subject to the constraints x + 2y ge 100, 2x - y le 0, 2x + y le 200, x, y ge 0 .

Graphically minimize and maximize z = 5x + 10y subject to the constraints: x +2y le 120, x+y le 60, x-2y ge 0 x, y ge 0 .

Minimize and Maximize Z=x +2y subject to the constraints x+2y ge 100, 2x-y le 0, 2x+y le 200, x, y ge 0

Maximize and minimize Z = 2x + 3y - 1 subject to the constraints x + y ge 5, x + y le 12, x le 10, y le 1 0, x, y ge 0 .

Maximize and minimize : Z = 15x + 30y subject to the constraints : x + y le 8, 2x + y ge 8, x - 2y ge 0, x, y ge 0 .

Graphically minimize and maximize z = 7x + 5y subject to the constraints: x+y le 50, x + 2y le 100, x -y ge 10 x, y ge 0 .