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`.

Maximize and minimize Z = 3x + 2y - 3 subject to the constraints x + y ge 4, x + y le 12, x le 9, y le 9, 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 .

Maximize Z = 22x + 44y subject to the constraints x + y ge 3, 3x + 8y le 24, x - y ge 0, x, y ge 0 .

Graphically minimize and maximize z = 3x + 4y subject to the constraints: x + y le 40 x + 2y le 80, x - 2y ge - 20 x, y ge 0 .

Graphically maximize the objective function Z = x + 2y subject to constraints x + 2y ge 100, 2x - y le 0, 2x + y le 200, x ge 0, y ge 0