Maximize `Z = 3x + 4y` subject to the constraints : `x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0` using graph.

Maximize Z = 7x + 4y subject to the constraints : 2x + y le 10, x + 2y le 12, x ge 0, y ge 0 using graph.

Maximize Z = 5x + 3y subject to the constraints : 2x + y le 8, x + 2y le 1 2, x ge 0, y ge 0 using graph.

Solve the following linear programming problem graphically : Minimize Z = - 3x + 4y subject to constraints x + 2y le 8, 3x + 2y le 12, x ge 0, 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 .

Solve the following linear programming problem graphically : Maximize : z = 3x + 2y subject to the constraints : x + 2y le 10, 3x + y le 15 ,x ge 0, y ge 0