Solve the following linear programming problem graphically. Maximize the objective function `Z = 8x + 9y` subject to the constraints `x + y le 6, x + 2y le 8, x ge 2, x ge 0, y ge 0`.

Solve the following linear programming problem graphically. Maximize the objective function Z = 9x + 10y subject to the constraints x + 2y le 6, x + y le 5, x ge 3, x ge 0, y ge 0 .

Solve the following linear programming problem graphically. Maximize the objective function Z = 2x + 6y subject to the constraints x + 2y le l 0, x + y le 7, x ge 2, x ge 0, y ge 0 .

Solve the following linear programming problem graphically. Minimize the objective function Z = 2x + 3y subject to the constraints x + y le 120, x + y ge 80, x le 80, y ge 60, x ge 0, y ge 0 .

Solve the following linear programming problem graphically. Minimize the objective function z = 2x + 3y subject to the constraints x + y le 100, x + y ge 60, x le 60, y le 50, x ge 0, y ge 0

Solve the following linear programming problem graphically. Minimize the objective function Z = 2x + 3y subject to constraints x + y le 80, x + y ge 40, x le 40, y ge 60, x ge 0, y ge 0

Graphically maximize the objective function Z = x + 2y subject to constraints 7x + 10y le 70, x - 2y ge 0, 2x + y ge 10, x ge 0, y ge 0

Graphically maximize the objective function Z = x + y subject to constraints 2x - y ge 0, 2x + y ge 8, 10x + 11y le 110, x ge 0, 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

Solve the following linear programming problem graphically : Maximize : z = 5x + 7y Subject to the constraints : x + 3 y le 60 ,x + y le 30,x ge 0, y ge 0