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 = 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 = 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 = 22x + 44y subject to the constraints x + y ge 3, 3x + 8y le 24, x - y ge 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 = 3x + 4y subject to the constraints : x + 2y le 8, 3x + 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.

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

Graphically maximize Z = 6x + 9y subject to the constraints 2x - y ge 0, 2x + y ge 8, x + 11 y le 80, x ge 0, y ge 0 .