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Introduction to Management Problems

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Problem 1
A graphical representation of a linear program is shown in the attachment. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
a) If this is maximization, which extreme point is the optimal solution? Explain your answer.
b) If this is a minimization, which extreme point is the optimal solution? Explain your answer.
c) What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Explain your answer.
d) Assuming this is a maximization problem, by how much can the coefficient of X in the objective function be increased before the optimal solution changes? Explain your answer.
e) Assuming this is a maximization problem, by how much can the coefficient of X in the objective function be reduced before the optimal solution changes? Explain your answer.

Problem 2

Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of rayon per week.

The table attached shows the relevant manufacturing information.

a) Formulate a linear program to maximize the company's profit and put it in standard format. Clearly define your decisions variables, objective function and constraints.
b) Implement your formulation in Excel and use Solver to find the optimal solution. Provide answers for the optimal amounts of different shirt types.
c) Based on the sensitivity analysis report, by how much can you reduce the price of the Athletic shirts before the optimal solution changes? Justify your answer.
d) In the optimal solution, how much more cotton and rayon would be left, if any?
e) If there is a 50% shortage in cotton and rayon, what impact does this have on your solution? Provide an explanation based on your current solution and not by resolving the problem.
f) If you can secure some free marketing only for one shirt type of your choice to increase its maximum weekly demand, which one would you choose and why?

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Solution Preview

Hi there,

Problem 1
a) If this is maximization, point E is the optimal solution.
The reason is the dashed line is furthest away from origin at point E and this leads to the maximal value for the objective function.

b) If this is a minimization, point B is the optimal solution.
The reason is the dashed line is closest to the origin at point A and leads to the minimal value for the objective function.

c) When the new slope of the objective function is same as the slope of AB, then the optimal solutions for the minimal values could be found in the line segment AB. In this ...

Solution Summary

An introduction to management problems are determined.

Similar Posting

Case: Introduction to Open Systems Theory SLP: Strategic Review


The case for this course is a little different from most classes, because it is an ongoing case analysis, and we call it the Integrative Case Project.

You will analyze one organization throughout the course, applying different models to assemble an organizational diagnosis. The organization will be National Presto Industries, Inc., identified as a leading company in Forbesâ?? 2010 Best Small Companies. http://www.forbes.com/lists/2010/23/best-small-companies-10_rank.html


Refer to the assigned and optional readings in the background for this module.


Oganizational Development (OD) and Open Systems Theory (OST)

In order to facilitate our integration of the various subject areas in the MBA degree, we will be using several models of organizational analysis and diagnosis. These models are based on open systems theory. You will review various OD models, some of which use OST as a framework for the model. So in this module we will be laying the foundation for the course with a brief introduction to systems theory and how it applies to organizations.

Assigned Readings:

Download and read this white paper by Falletta about OD models. Salvatore Falletta, President and CEO of Leadersphere, has written a white paper that reviews several commonly used models of organizational diagnosis. We will be using several of these models in conducting your integrative Case project. The relevant part of this paper in terms of this class are the first 31 pages. The last part of the paper (pp. 32 - 43) deals with the theoretical foundations of the Burke & Litwin model, Falletta's Organizational Intelligence Model, and reading that is optional. We are not covering Falletta's Org Intelligence Model. Note that on pages 8 and 9, Falletta discusses OST.

Falletta, S.V. (2005) Organizational Diagnostic Models: A Review and Synthesis. Retrieved 11/14/09 from http://www.leadersphere.com/img/OrgmodelsR2009.pdf

Optional Readings:

Faletta provides an overview OST in his paper (pp. 8 & 9). Keep in mind that OST is not an OD model, but is rather a basis for most of the later models.For a deeper understanding, go to this URL and read about systems, systems thinking, and organizations as open systems. You will see that businesses are not unlike living organisms. They depend on the environment for sustenance. They are comprised of multiple, mutually dependent parts. And they affect the environment in the course of their daily activities. Thus, organizations are open systems.

National Defense University, Systems Thinking and Learning Organizations, Retrieved 11/14/09 from http://www.au.af.mil/au/awc/awcgate/ndu/strat-ldr-dm/pt1ch4.html


Make a Case for which OD model you think is the best for doing an OD analysis for National Presto Industries, Inc., based on several current issues the company is facing. There are several parts to this assignment.


As the warrant for your case, explain the purpose and the value of conducting an OD diagnosis.
Then briefly evaluate each of the models presented in the background reading by Falletta. Omit Falletta's Org Intel model. Do NOT merely describe the models. You need to infer and comment on their strengths and weaknesses, and specifically indicate what type of organizational problem or functional area would benefit from an analysis using each model. This too will add to the warrant for your Case.
Now, Make a Case. Once you have discussed each of the eleven models, their strengths and weaknesses, and how they could best be applied, identify the model that you would choose for use in your analysis of the chosen company. First, introduce the company and describe its products/services. Then clearly explain the issues you are most concerned about. Then explain why your selection would be the best choice. You may want to find more data/information about the chosen model to make a stronger case with more backing.

This should be a 5 to 7 page paper (not including Title Page and References.) This paper is due by the end of the module.


Your paper will be evaluated on the following seven (7) points:

Precision - Does the paper address the question(s) or task(s)?
Breadth - Is the full breadth of the subject, i.e., all the keys to the assignment, addressed?
Depth - Does the paper address all elements of the topic in sufficient depth? Does it include and apply the background readings and other background resources? Are they included as references?
Critical thinking â?" Are the concepts of this module applied accurately, logically, and relevantly?
Organization - Is the paper organized in a coherent and systematic manner? Are headings included in all papers greater than 2 pages?
Clarity - Is the writing clear and the concepts articulated properly? Are paraphrasing and synthesis of concepts the primary means of response to the questions, or are thoughts conveyed through excessive use of quotations?
Referencing (citations and references) - Does the paper use citations and quotation marks where appropriate? Are all references listed in the bibliography used and referred to via citation?


The biggest problem students run into in this assignment is in simply describing the different models. In evaluating the models, be sure to go beyond mere description and discuss them in terms of strengths, weakness, similarities, differences, etc. Stress critical thinking! Use these insights to support and justify your assessment of which of these models is best for your chosen company.
Optimize your research time: Get an overview of the case assignments so you know what information you will be looking for when you do research. As you do research for Case 1, you can also be finding information and data for the other cases, too. Continue this strategy as you do research for the next case and the next, etc. The more information you have about the chosen company, the better you will get to know it. The better you get to know it, the better your analysis will be.
You may use a simple diagram to highlight important factors. However, do not use the diagram in lieu of valuable analysis (or to take up valuable writing space) - it should be in addition to your paper of 5-7 pages of analysis.
Just because you have written the minimum five pages does not mean that you have adequately covered the topic. Err on the side of writing more rather than less.
Choose the data you use carefully. Is it relevant and important?
Include a cover page and reference page, in addition to the 5-7 pages of analysis described above.
Include headings within the paper
Cite AND reference all sources that you use in your work, including those that you do not quote but paraphrase. This means include citations and quotation marks for direct quotes of more than 5 words, and citations for that information which you have "borrowed" or paraphrased from other sources.

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