MGT 3500 (74431-QTRA) Introduction to Management Science Benedetto C. Valenti Spring 2016 Assignment 1 Due Thursday, March 17 in class or by email to benedetto.valenti@baruch.cuny.edu Please answer the three questions below with specific and detailed reference to the data provided. No spreadsheet need be submitted if the formulas and the steps used are reported. In this case, label each cell with name and letter/number coordinates, and use these coordinates in each Excel formula. This is an individual assignment. You may discuss it with others, but never in front of a piece of paper, board, or screen. Refrain from sharing your final answers, since correct answers are not necessary to obtain a full score. Each Roman numeral holds up to one tenth of the full score. The full score is one tenth of your final score for this class. 1. You use an old cell phone for calls only and you have two options, buy a monthly plan or pay as you go. The phone plan costs $50 per month and calls are free up to 8 hours. Any extra minute for that month will cost you $0.25. Pay as you go has a flat rate of $0.15 per minute. (i) What are the two total costs if you plan to talk for 9 hours? Please, (ii) draw a single graph that shows the two options and clearly label the relevant points and ranges, (iii) and build a spreadsheet table that shows the same in table form. (iv) How should the fixed cost of the plan change so that the pay as you go option is always more convenient? (v) Considering only the cell phone plan with the $50 fixed cost and a 15-hour maximum talk time per month, optimize the average cost per minute with a method of your choice among a graph, an enumerative spreadsheet table or Excel Solver, along with a detailed explanation. 2. Suppose now that you buy a new smartphone that you will use for making calls and navigating the internet. Your only option is to buy a plan for $30 a month that also charges you $0.10 for each minute of conversation and $5 for each GB of data used. You need to talk for at least 7 hours a month and use at least 6GB of data. You also know that the sum of hours of talk time and GB of data will be at least 14. In order to find the least possible total cost you may spend per month, please (vi) define and write down the the decision variables, all the constraints and the objective function. Also, on a Cartesian plane (vii) draw the feasible region, locate the optimal solution and the binding constraints, and explain how these are connected in the phone plan context. 3. A telephone company has to determine the optimal cost structure of a phone plan. The plan will have a fixed cost and three unit costs, one for calls, one for data, and one for texts that customers have to pay for. These must range between $0 and $30, $0 and $0.10 per minute, $3 and $7 per GB and $0 and $0.20 per text, respectively. The objective is to maximize the revenue based on the typical customer who uses 9 hours of talk time, 4GB of data, and 200 texts. The typical customer does not want to pay for calls and texts more than she pays in fixed cost, does not want the data cost to exceed 50% of the total cost, and does not want to pay more than $40 for fixed and data cost combined. Please, (viii) find the optimal solution. For all binding and not-binding constraints, (ix) write what happens to the optimal value of the objective function when you change their right-hand-side parameter by 1 or 1. (x) Change one one of these parameters so that the feasible region becomes empty and Solver is not able to find a solution. Explain why that happens