Problem 1:
Consider the following linear programming problem.
Minimize Z = 5x1 + 6x2 + 3x3,
Subject to:
5x1 + 5x2 + 3x3 ≥ 50
x1 + x2 - x3 ≥ 20
7x1 + 6x2 -9x3 ≥ 30
5x1 + 5x2 + 5x3 ≥ 35
2x1 + 4x2 -15x3 ≥ 10
12x1 + 10x2 ≥ 90
x2 -10x3 ≥ 20
x1, x2, x3 ≥ 0
a) In an Excel workbook, solve the problem by using the Solver. Generate the Solver sensitivity and answer reports.
b) In this Word document, write the mathematical formulation of the dual problem. Generate a sensitivity report of the dual problem.
Solve the dual problem in another sheet of the same Excel file.
c) In this Word document, describe whether the solution of the dual problem offers computational advantage and explain why. Submit the Excel workbook as a separate attachment
Problem 2:
Consider the following LP problem.
Maximize Z = 2x1 + 4x2 + 4x3 -3x4,
Subject to:
x1 + x2 + x3 = 4
x1 + 4x2 + x4 = 9
x1, x2, x3, x4 ≥ 0
Using x3 and x4 as starting variables, the optimal tableau is given as:
| Basic |
x1 |
x2 |
x3 |
x4 |
Solution |
| Z |
2 |
0 |
0 |
3 |
16 |
| x3 |
0.75 |
0 |
1 |
-0.25 |
2 |
| x4 |
0.25 |
1 |
0 |
0.25 |
2 |
In this document, write the formulation of the associated dual problem.
In this document, determine the optimal solution to the dual problem in two ways
Problem 3:
Bag Company produces leather jackets and handbags. A jacket requires 8 m2 of leather and a handbag only 2 m2. The labor requirements for the two products are 12 and 5 hours respectively. The current weekly supplies of leather and labor are limited to 1,200 m2 and 1,850 hours. The company sells the jackets for $350 and the handbags for $120. The objective is to determine the production schedule that maximizes the net revenue.
In this document, write the mathematical formulation of both the primal and the dual problems.
In the Excel file used in problem 1, solve the primal problem and generate a Solver sensitivity report in a new worksheet.
In this document, use the Solver sensitivity report to answer the following two questions:
What is the maximum purchase price the company should pay for additional leather?
What is the maximum amount the company should pay for additional labor?