Solve the following linear programming problem graphically: Maximize Z = 7x + 10y subject to the constraints 4x + 6y ≤ 240, 6x + 3y ≤ 240, x ≥ 10, x ≥ 0, y ≥ 0

The LPP given is: Maximize 7x + 10y subject to constraints 4x + 6y ≤ 240 ⇒ 2x + 3y ≤ 120, 6x + 3y ≤ 240 ⇒ 2x + y ≤ 80, x ≥ 10, y ≥ 0
Plot the graphs of 2x + 3y = 120, 2x + y = 80, x = 10. The shaded portion is the feasible region of the solution.
The corner points of the feasible region are (10, 0), (40, 0), (30, 20) and (10, 100/3)
Examining the objective function at these values:
(x, y) Value of objective function: 7x + 10y
(10, 0) 70
(40, 0) 280
(30, 20) 410
(10, 100/3) 403.33
From the values, we can see that 7x + 10y is maximum when x = 30, y = 20. The maximum value is 410.