southern new hampshire university mat 410 module four problem set 1 fo

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Southern New Hampshire University
MAT 410 Module Four Problem Set
1. For the following three problems, provide your written solutions within this template. Do not create a new file.
2. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
3. Provide formulas using Equation Editor and diagrams using Drawing Tool.
4.
Use the Solver to obtain computer solutions in an Excel workbook.
5. Submit the Word and Excel workbook(s) separately as attachments.
Problem 1
Consider the following linear programming problem.
Minimize Z = 5×1 +6x2 + 3 x3,
Subject to:
5x15x2 + 3 x3 ≥ 50
X1 + x2 − X3 ≥ 20
7x1 + 6×2 - 9x3 ≥ 30
5x1 +5x2+5x3 ≥ 35
2x1 + 4x2 - 15 x3 ≥ 10
12 x1 + 10 x2 ≥ 90
X2-10 x3 ≥ 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.
c) Solve the dual problem in another sheet of the same Excel file.
d) 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.
Source: Modified from Taha, H. A. (2017). Operations research: An introduction (10th ed.), Problem 4-11, p. 164.
Copyright 2017 by Pearson.
Write your responses to parts (b) and (d) in the space provided:
a) Excel Solver solution (submit your Excel workbook separately)
b)
c) Excel solution (submit your Excel workbook separately)
d)
Problem 2
Consider the following LP problem.
1 Southern New Hampshire University
Maximize Z = 2x1 + 4x2 + 4x3 - 3×4,
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
Xa
Solution
Z
2
0
0
3
16
X3
0.75
0
1
-0.25
2
X
0.25
1
0
0.25
2
a) In this document, write the formulation of the associated dual problem.
b) In this document, determine the optimal solution to the dual problem in two ways.
Source: Modified from Taha, H. A. (2017). Operations research: An introduction (10th ed.), Problem 4-14, p. 165.
Copyright 2017 by Pearson.
Write your responses to parts (a) and (b) in the space provided:
a)
b)
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.
a) In this document, write the mathematical formulation of both the primal and the dual problems.
b) In the Excel file used in problem 1, solve the primal problem and generate a Solver sensitivity report in a new
worksheet.
c) In this document, use the Solver sensitivity report to answer the following two questions:
i. What is the maximum purchase price the company should pay for additional leather?
ii.
What is the maximum amount the company should pay for additional labor?
2 Southern New Hampshire University
Source: Modified from Taha, H. A. (2017). Operations research: An introduction (10th ed.), Problem 4-30, p. 170.
Copyright 2017 by Pearson.
Write your responses to parts (a) and (c) in the space provided:
a)
b) Excel Solver solution (submit your Excel workbook separately)
c)
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