Maximize `Z = 12x + 24y` subject to the constraints `x + y ge 5, 5x + 7y le 35, x - y ge 0, x, y ge 0` graphically.

Maximize Z = 52x + 26y subject to the constraints x + y ge 5, 5x + 8y le 40, x - y ge 0, x, y ge 0 graphically.

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

Maximize Z = 6x + 8y subject to the constraints x + y le 6, 3x + y ge 6, x - y ge 0, x, y ge 0 graphically.

Maximize Z = -x + 2y, subject to the constraints : x ge 3, x + y ge 5, x + 2y ge 6, y ge 0.

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

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 .