Question

1. Consider the following linear programming problem, and find the solution graphically in excel.

                        Maximize                     4X + 10Y

                        Subject to:                    3X + 4Y <= 480

                                                            4X + 2Y <= 360

                                                            2X + 3Y >= 90

                                                            all variables >= 0

Answer 1

To find the solution, we can find plot the given constraint on the graph and the find the feasible solution area. We then find the value of the objective function at the corner points of the feasible solution. The point where the objective function has the maximum value is the solution.

The graph of the equation and the feasible area is shown in the below image

We can see that there are 5 corner points of the feasible solution.

A (0,120), B(48, 84) C(90,0) D(45,0) E (0,30)

We find the value of objective function 4X+10Y at each of the corner points

Value at A (0,120) : 4*0+10*120 = 1200

Value at B (48,84) : 4*48+10*84 = 1032

Value at C (90, 0) : 4*90+10*0 = 360

Value at D (45,0) : 4*45+10*0 = 180

Value at E (0,30) : 4*0+10*30 = 300

We can see that the maximum value of objective function occurs are A (0,120).

Hence the solution is X = 0 and Y =120. The value of objective function at optimal solution is 1200.