Decision Models & Analytics Final Exam
决策模型与分析考试代写 For the third problem, please make sure you submit both the complete Excel sheets and all the relevant plots.
1.You have 1 hour and 50 minutes to complete this exam. When you are finished, please submit your solutions electronically to NYU Classes.
2.You are NOT allowed to use material other than the course materials during the exam. Do not use the Internet and/or talk to anyone during the exam. Please respect the honor code.
3.The exam has 3 problems and is worth 100 points. The first problem is worth 35 points, the second problem is worth 30 points and the third problem is worth 35 points. For the third problem, Part a) is worth 20 points, and Part b) is worth 15 points. 决策模型与分析考试代写
4.For the third problem, please make sure you submit both the complete Excel sheets and all the relevant plots.
5.Please show all of your work. Do not expect the grader to guess your reasoning. Your grade on the exam will depend on the clarity of your answers, the reasoning you have used, and the correctness of your answers.
1.A supermarket chain is deciding which locations to open in Middletown.
Its stores earn an average of $80 per year per regular customer. The following is a map with the number of regular customers it expects to attract in each district.
If it opens a store in a given district, then the store will attract all the customers it expects there.
If there is no store in a district, but there is a store in a neighboring district, then the store will attract 40% of those customers. Customers will not travel a distance greater than one district (horizontally or vertically on the map, not diagonally) to go to a store. Given that each store costs 900 thousand dollars a year to operate, the supermarket chain would like your help in deciding in which locations to open its stores. Do not use any nonlinear formulation. Submit both the math modelling and the completed Excel sheet. 决策模型与分析考试代写
2.Suppose there are 5 currencies available (US Dollars, Japanese Yens, British Pounds, Swiss Francs and Euros) and assume that one unit of currency i can be exchanged for ri,junits of currency j. You work in a hedge fund and you found a profitable investment opportunity in a market in Germany and to invest in it, you need to convert as much money as you can from dollars (currency 1) to euros (currency 5). You have access to 10 million dollars that you can use to make this investment. However, your hedge fund also implements controls that limit your ability to buy foreign currencies. You cannot trade more than Ki,j from currency i to currency j in a single day, where Ki,j is measured in currency i.
Can you create a linear optimization model to find the maximum amount of euros that you can obtain within a single day? Do not use any nonlinear formulation. Only math modelling is needed (i.e. no need for Excel).
3.As the manager of a credit card services at the Bank of Hanover (BOH), you are aware that the average profitability of a credit card customer grows with the number of years they have used the credit card. 决策模型与分析考试代写
Two probabilistic factors affect actual profitability. The mean profitability function is given in the table below, which has been gathered from data on BOH customers.
The actual profit in a given year follows a normal distribution, with a standard deviation equal to 25% of the mean profit. In addition, there is a probability that a customer will continue to use the card during year t. This probability is sometimes called the retention rate. For instance, an 80% retention rate means that, during any year, there is a 20% chance that the customer will cancel their credit card. Assume that if a customer cancels during year t, then the cancellation occurs at the end of the year, and BOH still gets the profit from year t but no more profits after year t. The current retention rate has been estimated at 80%. BOH uses a discount rate of 10% to calculate net present values.
(a)What are the expected value and the standard deviation of the NPV from a customer? In running the simulation, use a sufficient number of trials to estimate the expected NPV from a customer within $1 with 95% confidence (i.e., make sure that the length of 95% confidence interval does not exceed$2).
(b)What is the probability that the NPV for a given customer will exceed$100?