Business Applications of Decision Sciences

Questions are attachedInstructions: 1. No graphing calculator is allowed. Please DO NOT USE EXCEL OR ANY COMPUTER SOFTWARE OR WEBSITE to solve the problems or to draw graphs. If you answer any question using a graphing calculator, software or a website, you will not receive any credit for it. 2. Show all work. Just writing the final answer will not get you full credit. 3.Make sure you have answered all six questions. 4. Please submit the exam in Microsoft Word. 1. (a) What is a transportation problem? Briefly discuss the decision variables, the objective function and constraint requirements in a transportation problem. Give a real world example of the transportation problem. (b) What is a marketing problem in applications of linear programming? Briefly discuss the decision variables, the objective function and constraint requirements in a marketing problem. Give a real world example of a marketing problem. (c) What are the differences between QM for Windows and Excel when solving a linear programming problem? Which one you like better? Why? (d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.
exam2__3_.doc

Unformatted Attachment Preview

Don't use plagiarized sources. Get Your Custom Essay on
Business Applications of Decision Sciences
Just from $13/Page
Order Essay

OPRE 315
Business Applications of Decision Sciences
Instructions:
1. No graphing calculator is allowed. Please DO NOT USE EXCEL OR ANY COMPUTER
SOFTWARE OR WEBSITE to solve the problems or to draw graphs. If you answer any question
using a graphing calculator, software or a website, you will not receive any credit for it.
2. Show all work. Just writing the final answer will not get you full credit.
3. Make sure you have answered all six questions.
4. Please submit the exam in Microsoft Word.
1. (a) What is a transportation problem? Briefly discuss the decision variables, the objective function and
constraint requirements in a transportation problem. Give a real world example of the transportation problem.
(b) What is a marketing problem in applications of linear programming? Briefly discuss the decision variables,
the objective function and constraint requirements in a marketing problem. Give a real world example of a
marketing problem.
(c) What are the differences between QM for Windows and Excel when solving a linear programming
problem? Which one you like better? Why?
(d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations
to the decision maker? Give a real world example.
1
Answer Questions 2 and 3 based on the following LP problem.
Maximize 8C + 10R + 7T
Subject to
7C + 10R + 5T = 2000
2C + 3R + 2T = 660
C = 200
R = 300
T = 150
And C, R, T = 0
Total profit
Production budget constraint
Labor hours constraint
Maximum demand for clocks constraint
Maximum demand for radios constraint
Maximum demand for toasters constraint
Non-negativity constraints
Where C = number of clocks to be produced
R = number of radios to be produced
T = number of toasters to be produced
The QM for Windows output for this problem is given below.
Solution List:
Variable
Status
C
Basic
R
NONBasic
T
Basic
slack 1
NONBasic
slack 2
Basic
slack 3
Basic
slack 4
Basic
slack 5
NONBasic
Optimal Value (Z)
Value
178.57
0
150
0
2.86
21.43
300
0
2478.57
2
Linear Programming Results:
C
Maximize
8
Constraint 1
7
Constraint 2
2
Constraint 3
1
Constraint 4
0
Constraint 5
0
Solution
178.57
R
10
10
3
0
1
0
0
T
7
5
2
0
0
1
150
Ranging Results:
Variable
Value
C
178.57
R
0
T
150
Reduced Cost
0
1.43
0
Slack/Surplus
0
2.86
21.43
300
0
Constraint 1
Constraint 2
Constraint 3
Constraint 4
Constraint 5
Dual Value
1.14
0
0
0
1.29
RHS
Dual
<= <= <= <= <= 2000 660 200 300 150 2478.57 1.14 0 0 0 1.29 Original Val 8 10 7 Lower Bound 7 -Infinity 5.71 Upper Bound 9.8 11.43 Infinity Original Val 2000 660 200 300 150 Lower Bound 750 657.14 178.57 0 120 Upper Bound 2010 Infinity Infinity Infinity 155 2. (a) Determine the optimal solution and optimal value and interpret their meanings. (b) Determine the slack (or surplus) value for each constraint and interpret its meaning. 3. (a) What are the ranges of optimality for the profit of a clock, a radio and a toaster? (b) Find the dual prices of the five constraints and interpret their meanings. Determine the ranges in which each of these dual prices is valid. (c) If the profit contribution of a clock changes from $8 to $9, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the ranging results given above). (d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the ranging results given above.). 4. A campus dietitian for a college wants to formulate a nutritious meal plan for students. She wants to satisfy the following requirements: - at least 2400 calories - at most 2600 calories - no more than 60 grams of fat - at least 28 grams of protein - no more than 100 grams of carbohydrates. On a particular day, her food stock includes five items that can be prepared and served to meet these requirements. The cost per pound for each food item and the contribution to each of the four nutritional requirements are given in the table below. 3 Food Beef Chicken Beans Arugula Potatoes Calories /pound 400 360 130 100 320 Fat grams/pound 12.3 10.5 1.1 1.0 0.8 Protein grams/pound 70 65 14 12 6 Carbohydrates grams/pound 0 0 40 22 75 Cost Dollars/pound 2.20 2.50 0.85 2.40 0.50 Formulate a linear programming model that meets these restrictions and minimizes the total cost of the meal by determining (a) The decision variables. (Hint: There are 5 decision variables.) (b) The objective function. What does it represent? (c) All the constraints. Briefly describe what each constraint represents. (Hint: There are 5 constraints in addition to non-negativity constraints.) Note: Do NOT solve the problem after formulating. 5. An oil company wants to decide how to allocate its budget. The government grants certain tax breaks if the company invests funds in research concerned with energy conservation. However, the government stipulates that at least 35 percent of the funds must be funneled into research for automobile efficiency (methanol fuel research and emission reduction). The company has a budget of $2.5 million for investment. The research proposal data are shown in the following table. Maximum Investment Annual Return Project Allowed on Investment ______________________________________________________________ Methanol fuel research $800,000 2.3% Emission reduction $500,000 2.2% Solar cells $700,000 2.8% Windmills $620,000 2.6% ______________________________________________________________ The company wants to receive the government tax break. How much money should be invested in each project if the company wants to maximize total annual return on its investments? Formulate a linear programming model for the above situation. (a) Define the decision variables. (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating. 4 6. A software development company wants to assign 5 software engineers to four projects. The estimated time of completion (in days) of each project by each software engineer is given in the following table. Project 1 Project 2 Project 3 Project 4 ___________________________________________________________ Software Engineer A 30 25 17 14 Software Engineer B 40 30 22 32 Software Engineer C 38 19 22 Software Engineer D 32 25 15 19 Software Engineer E 35 24 15 20 ___________________________________________________________ Software engineer C cannot be assigned to project 2 because she does not have enough training to do that project. The company wants project 4 to be assigned to software engineer A or software engineer B. The objective is to minimize the total time of completion of all four projects. For this assignment problem: (a) Define the decision variables. (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating. 5 ... Purchase answer to see full attachment

GradeAcers
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.

Order your essay today and save 15% with the discount code DISCOUNT15