Problem Set
1. For all the following problems, word-process your 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. Word-process formulas using Equation Editor and diagrams using Drawing Tool.
4. Use Solver to obtain computer solutions in an Excel workbook.
5. Submit the Word and the Excel workbook(s) separately as attachments.
Problem 1
Determine the optimum solution for each of the following LPs by enumerating all basic solutions.
Maximize Z = 2x1 -4x2 + 5x3 - 6x4,
Subject to:
x1 + 4x2 - 2x3 + 8x4 ≤ 2
-x1 + 2x2 + 3x3 + 4x4 ≤ 1
x1, x2, x3, x4 ≥ 0
Minimize Z = x1 + 2x2 - 3x3 - 2x4,
Subject to:
x1+ 2x2 - 3x3 + x4 = 4
x1+ 2x2 + x3 + 2x4 = 4
x1, x2, x3 , x4 ≥ 0
Source: Operations Research, An Introduction by Taha. Ninth Edition. Chapter 3 Page 75 Pearson. 2011
Write your responses to parts (a) and (b in the space provided below:
Problem 2
Consider the following sets of constraints:
x1 + 2x2 + 2x3+ 4x4 ≤ 40
2x1 -x2 + x3 + 2x4 ≤ 8
4x1 - 2x2 + x3 -x4 ≤ 10
x1, x2, x3 ,x4 ≥ 0
Use the Simplex iteration method to solve the problem for each of the following objective functions.
Maximize Z = 3x1-x2 + 3x3 + 4x4.
Minimize Z = 5x1 - 4x2 + 6x3 -8x4.
Write your responses to parts (a) and (b) in the space provided below:
Problem 3
The Gutuchi Company manufactures purses, shaving bags and backpacks. The construction includes leather and synthetics. Leather being the scarce raw material.
The production process requires two types of skilled labor: sewing and finishing.
The following table gives the availability of the resources, their usage by these products, and the profits per unit. The production manager at Gutuchi wishes to determine the production levels so that the company's total revenue is maximized.
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** Resource Required per Unit **
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Resource:
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Purse
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Bag
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Backpack
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Daily Availability
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Leather (Sq. ft.)
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2
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1
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3
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42
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Sewing (Hr.)
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2
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1
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2
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40
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Finishing (Hr.)
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1
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0.5
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1
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45
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Selling Price ($)
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24
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22
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45
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(a) In this document, describe the components (decision variables, the objective function, and the constraints) in the context of this problem.
(b) In this document, write the mathematical formulation of the problem.
(c) In this document, address the manager's concern by describing the solutions obtained fromthe Solver.
(d) In an Excel workbook, solve the problem by using the Solver.