Question

Consider the following linear programming problem:

                  Maximize Profit    30X + 50Y

                  Subject to              4X +   5Y = 40,000

                                                               X ≥   3,000

                                                               Y ≥   4,000

                                                    X ≥ 0 and Y ≥ 0

1. Use a graph to show each constraint and to identify feasible region.
2. Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?
3. From your graph, what is the optimal value of the objective function?

Answer 1

here using given LPP we find optimal solution by ghraphical method for simplicity we take X= x1 and Y= x1 and find the solution

Here we gate the value of X = x1 = 3000 and Y = x2 = 5600

then put this value in the objective function Maximize Profit = 30X + 50Y

Therefore maximum profit = (30 * 3000) + (50 * 5600)

Hence Mxa Z = Maximum profit = 370000

Thank You..!!

Please like it..