Consider the following cost minimization linear programming problem:
LINEAR PROGRAMMING PROBLEM
Max: 41X1 + 32X2 + 75X3
Subject to:
3X1 + 5X2 + 2X3 ≥ 120 …… (1)
6X1 + 7X2 + 8X3 ≤ 264 …… (2)
5X1 + 3X2 + 3X3 ≤ 135 …… (3)
a) Use Lingo or any other LP software legally available to you to find a solution for this problem. Provide all your output.
b) What is the optimal solution and the objective function value for this problem?
c) What will the profit on a unit of X3 have to be before X3 will have a positive value in the optimal solution?
d) Interpret the dual prices of the three constraints.
e) Indicate which constraints are binding and why they are binding.
f) Explain fully what would happen if the objective function coefficient of X1 is increased by 50.
g) Explain fully what would happen if the right hand sides of constraints 1 and 2 were increased by 50 units and 30 units respectively.