Linear Programming models

Take Home Final Exam Answer Sheet

Professor:	Dr. Erman COSKUN	Name:
Class:	EMBA 2021	Student ID:
Class:	QM 511	Date:

Instructions:

1. ALL WORK MUST BE YOUR OWN. I DO NOT WANT COPY-PASTE ANSWERS OR BOOK DEFINITIONS. FOR QUESTION-1 and WHERE APPROPRIATE YOU MUST PROVIDE REFERENCES YOU ARE USING. FOR DEFINITIONS YOU CAN USE SOURCES BUT FINAL ONE YOU ARE USING SHOULD BE YOUR OWN.

2. I DO NOT want any Excel file. You must copy-paste screen shots of your Excel solutions to this document.

3. Once you are done upload this answer sheet on Black Board.

4. Deadline Nov 16 (Tuesday) 23:59 PM.

5. Maximum temps to upload: 2 (In case you encounter some technical issues)

6. You have to complete this exam answer sheet by yourself. Academic honesty is very important and all kind of checks related to academic integrity and plagiarism will be made by the instructor.

7. No late submission will be accepted under any circumstance. So please do not wait until last minute to avoid from technical problems and difficulties.

8. Submit ONLY your Word file. For Excel solutions put SCREEN SHOTS as pictures.

Question 1:

This should be about two or three paragraphs or no more than a one-sided page in length. You should use your own words and comments and not those of the text or anyone else.

a) In your own words briefly discuss the essentials and importance of Linear Programming models and how they are used in the business world. What are the pros and cons of linear programming. Give an example of their use in functional business areas like Marketing, Production, Finance, Human Resources. (10 POINTS)

b) Please tell me your understanding of what is sensitivity analysis in linear programming problems? What is the definition of shadow price? What is the managerial use of sensitivity analysis and shadow prices? Find an example (from any source) and clearly explain sensitivity analysis and shadow prices on it by using managerial approach. Your example must be meaningful for explaining sensitivity analysis. (10 POINTS)

Answer-1

Question 2:

Suppose you own an expensive car and purchase auto insurance. This insurance has a $1000 deductible, so that if you have an accident and the damage is less than $1000, you pay for it out of your pocket. However, if the damage is greater than $1000, you pay the first $1000 and the insurance pays the rest. In the current year there is probability 0.025 that you will have an accident. If you have an accident, the damage amount is normally distributed with mean $3000 and standard deviation $750.

a) Use Excel to simulate the amount you have to pay for damages to your car. This should be a one-line simulation, so run 5000 iterations by copying it down. Then find the average amount you pay, the standard deviation of the amounts you pay, probability of making a payment for you in that year (Note that many of the amounts you pay will be 0 because you have no accidents.)

b) Continue the simulation in part a by creating a two way data table, where the row input is the deductible amount, varied from $500 to $2000 in multiples of $500. Now find the average amount you pay, the standard deviation of the amounts you pay. (20 POINTS)

Answer-2

Question 3:

Please go over BLENDING AT CHANDLER OIL from our textbook. Pg 639. I know that the solution is already there. I want you to look at the question, understand it. Look at the book design and solution of problem provided in the book and understand it. Then close the book and design it by yourself and develop your own MODEL. If you have difficulty you can revisit the book solution and comeback to your own design. So, only copy and pasting will not help, I want to see your design. Of course the results will be same as book but your design will be different. (20 POINTS)

Answer-3

Question 4

You are high level decision maker for a production company. You produce and export your products. You are aware of uncertainty in the market and trying to predict your end of 2021 profit.

* From analysis of past contracts and documents you found out that average price for the past was SAR 37.5, and that prices of individual sales is uniformly distributed between SAR 35 and 40

* Your marketing and sales manager forecasts that your sales number would be 1.1 million units for 2021 with standard deviation of 180000 units. Sales quantity is normally distributed.

*Raw material and transportation are variable costs. Based on past data, these costs are equal to an average of 50% of the sales price. The standard deviation of variable costs is 10% and it is normally distributed.

* There are fixed cost items such as managerial costs and salaries. They are calculated based on SAR and they are uniformly distributed between 25.000.000 - 35.000.000 SAR Please use Monte Carlo Simulation and answer below questions.

a) What is the simulated chance of making a profit in 2021?

b) What is the expected profit?

c) A business partner offers to take over the business for one year for 20 million SAR. Should you take the deal? Why /why not? Please put screen shot of Excel file with simulated results. (20 POINTS)

Answer-4

Question-5

You must use the provided data file for this question. The data file provided in BB page under content section. The file name is Data for House Prices.

A) Based on provided data set do the selling prices of houses in a given community vary systematically with their

a) sizes (as measured in square feet),

b) lot size, and

c) number of bathrooms?

Answer this question by estimating a simple regression equation for each independent variable. Interpret your estimated equation and the associated R2 . Please interpret which one out of these three independent variables would be a better estimator for house selling price? Why?

B) Please try to use a multiple linear regression with all these three independent variables. Create the regression model and write the equation. (20 POINTS)

Answer -5