Final exam for course Data optimization. The exam will last 3 hours, both excel and python will be used.Attach exam study guide.
Data Optimization Prof. Rolleigh Exam Study Guide General Information/Tips: The Exam is 3 hours long at the time scheduled on Canvas. Proctorio will be turned on for the exam. The exam is open note, open internet, open book, etc. The only resource you cannot use is other people. Proctorio will allow new browser tabs and copy/paste. Feel free to use old code or Excel files if they are helpful. You can answer questions using Excel or python. I think Excel is faster for most people, but do whatever you are more comfortable with. The exam will be done entirely in Excel. You can do work in python and copy/paste your answers into the excel file. I will post an example template so you are not surprised on the day of the exam. I STRONGLY suggest you look over the example template and read the instructions. Basically answer the questions in the shaded red areas. Don’t write on the answer sheet tab, the red shaded areas will send the answers there. There will be some multiple choice (10-15) and some longer problems. You will probably have to do some work for some of the multiple choice. Expect to spend the full 3 hours on the exam. This practice exam is roughly the length of the exam. Expect 5 more multiple choice on the exam. The longer problems are 60-75% of the exam grade. Unlike my usual exams, I will award partial credit on code written and/or models built in Excel. You do not have to have it 100% correct. I think I will have you upload any code separately, but I need to make sure Canvas will do that well on an exam. You should be able to: 1. Interpret the output from Solver Answer and Sensitivity reports 2. Interpret the output from PuLP 3. Answer conceptual questions about any of the class content 4. Set up and solve a simple LP in Excel or python 5. Set up and run a simple Monte Carlo in Excel or python 6. Set up and solve a simple Non Linear Program in Excel (or python if you really want to) 7. Understand conclusions from Chapter 1 of Algorithms to Live By Multiple Choice Practice Questions: 1. A section of the Sensitivity report from Excel shows: Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $I$2 A 0 - 0.828507795 10 0.828507795 1E+30 $I$3 B 570.0 0 13 1E+30 0.039175258 $I$4 C 0 - 0.042316258 14 0.042316258 1E+30 What will happen if the Coefficient on A in in the Objective Function is increased by 0.5? a) Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same. b) The value of the objective function will change, but the values of the decision variables and shadow prices will remain the same. c) The same decision variables will be positive, but the values of the objective function, decision variables, and shadow prices will all change. d) We must resolve the problem to answer this question. 2. This question also refers to the output above. What happens to the optimal value of C if the coefficient on C in the objective function decreases by 1? a) Optimal value of C will fall b) Optimal value of C will rise c) Optimal value of C will remain the same d) Not enough information given 3. A constraint with a non-zero slack value is best described as: a) We are not using all of those resources, and the constraint has a non-zero shadow price b) We are not using all of those resources, and the constraint has a 0 shadow price c) We need to add more of this resource to improve the value of the objective function d) We do not need more of this resource, as the shadow price is non-zero 4. In the OJ Dataset, which of the below are choice variables? a) All the prices b) All the marketing strategies (feat and display) c) Price 5 d) The unit sales for all SKU’s e) Both a and b 5. The improvement in the objective function per unit increase in the RHS of a constraint is the: a) Sensitivity value b) Reduced cost c) Constraint coefficient d) Shadow price 6. The amount that the objective function coefficient of a decision variable would need to improve before that variable would have a positive optimal value is the a) Shadow Price b) Surplus Variable c) Reduced Cost d) Upper Limit 7. Which of the following is usually not a Linear Programming Problem? a) Profit Maximization b) Shipping Cost Minimization c) Profit Maximization with a Downward Sloping Demand d) Workforce Assignment 8. Which of the following is true about Linear Programming problems? a) The answers are usually on the corners of the feasible set b) The answers are usually unique c) The feasible set is a polytope d) All of the above e) None of the above 9. Which of the following is true about Non-Linear Programming Problems? a) They find global maximums b) They handle corner solutions well c) They are faster to solve than Linear Programming Problems d) All of the Above e) None of the Above 10. Suppose you ran a regression of the form ??(?????5) = ?0 + ?1??(?????5) ?0 = 4, ?1 = −2.5 If the company lowers price by 10%, what happens to sales5? a) Sales5 increase by 10% b) Sales5 decrease by 10% c) Sales5 increase by 25% d) Sales5 decrease by 25% e) Not enough information given Longer Answer (Problems): 1. Suppose an Air Conditioning manufacturer produces three home air conditioners: Economy, Standard, and Deluxe. Profits per unit are 63, 95, and 135 dollars, respectively. The production requirements per unit are: Fans Used Cooling Coils Used Labor Used Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the next production period, the company has 200 Fans, 320 Cooling Coils, and 2400 hours of labor. What should the company produce to maximize profits? Solve in Excel or PuLP. What are the shadow prices for each resource? What is the maximum the firm should be willing to pay for an hour of overtime? Should the company hire 200 additional hours at that price? 2. Use the OJ or Milk Dataset to run a regression predicting sales. ??(?????5) = ?0 + ?1??(?????5) Assume a constant gross margin for SKU5 equal to its historical average. Set up a profits model in Excel where you estimate quantity sold using the regression, multiply quantity sold times price to get revenues, and find profits using total revenues * gross margin. What is the price5 that maximizes profits? What is the price5 that maximizes total revenues? Explain in a sentence or two how you could improve the model. 3. Suppose you work as an analyst for a firm producing cute customized notebooks to sell on Etsy as fake handmade crafts (this is slightly unethical, but ethics is not part of this problem). Your company is especially worried about losses and wants to know what the risks of losing money are for a price of $25 per notebook. Demand is uncertain, and they ask you to build a Monte Carlo simulation to determine what fraction of the time you lose money. 1000 simulations is fine. We know that fixed costs are $5,000 for product development. Variable costs are $10 per notebook from your factory in Guangzhou. We estimate demand to be a normally distributed variable with mean = 10,000 and standard deviation = 3000. Write a Monte Carlo simulation to find the fraction of the time we lose money. What are the average profits exactly? What is your estimate from the Monte Carlo for Average Profits? Multiple Choice Practice Questions Answers: 11. A section of the Sensitivity report from Excel shows: Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $I$2 A 0 - 0.828507795 10 0.828507795 1E+30 $I$3 B 570.0 0 13 1E+30 0.039175258 $I$4 C 0 - 0.042316258 14 0.042316258 1E+30 What will happen if the Coefficient on A in in the Objective Function is increased by 0.5? e) Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same. f) The value of the objective function will change, but the values of the decision variables and shadow prices will remain the same. g) The same decision variables will be positive, but the values of the objective function, decision variables, and shadow prices will all change. h) We must resolve the problem to answer this question. Copy paste redid my lettering for answers. Please ignore that. I provide the original lettering answer as well as the updated lettering answer. Answer: A (or e after copy/paste). The change is less than the reduced cost or allowable range, so it does not change anything. We still make 0 of product A. 12. This question also refers to the output above. What happens to the optimal value of C if the coefficient on C in the objective function decreases by 1? e) Optimal value of C will fall f) Optimal value of C will rise g) Optimal value of C will remain the same h) Not enough information given Answer: C or G. Nothing changes, as we made 0 C before and now it is even less valuable. 13. A constraint with a non-zero slack value is best described as: e) We are not using all of those resources, and the constraint has a non-zero shadow price f) We are not using all of those resources, and the constraint has a 0 shadow price g) We need to add more of this resource to improve the value of the objective function h) We do not need more of this resource, as the shadow price is non-zero Answer: B or F.