A marketing company must decide how many interviews to conduct during daytime (their number is D) and how many during the evening (their number is E). At least 70% of the interviews have to be during day time. A correct modeling of this constraint is O 3E >= 7D O 3E <= 7D O 3D<=7E O 3D >= 7E
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- You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then from the proposed ratings, you predict whether the home team will win. (You predict the home team will win if the home team advantage plus the home teams rating is greater than the visitor teams rating.) You want the ratings such that the number of predictions that match the actual outcomes is maximized. Try modeling this. Do you run into difficulties? (Remember that Solver doesnt like IF functions.) EXAMPLE 7.8 RATING NFL TEAMS9 We obtained the results of the 256 regular-season NFL games from the 2015 season (the 2016 season was still ongoing as we wrote this) and entered the data into a spreadsheet, shown at the bottom of Figure 7.38. See the file NFL Ratings Finished.xlsx. (Some of these results are hidden in Figure 7.38 to conserve space.) The teams are indexed 1 to 32, as shown at the top of the sheet. For example, team 1 is Arizona, team 2 is Atlanta, and so on. The first game entered (row 6) is team 19 New England versus team 25 Pittsburgh, played at New England. New England won the game by a score of 28 to 21, and the point spread (home team score minus visitor team score) is calculated in column J. A positive point spread in column J means that the home team won; a negative point spread indicates that the visiting team won. The goal is to determine a set of ratings for the 32 NFL teams that most accurately predicts the actual outcomes of the games played.Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.
- A company has one machine which can be used to make product Alpha and product Beta. Each unit of product Alpha requires 45 minutes of machine time, while each unit of product Beta requires 37 minutes of machine time. The machine can be used for 8 hours per day and 5 days per week. Next week the company will produce 23 units of product Alpha. After completing the production of Alpha, the company will produce product Beta. How many units of product Beta can be produced next week? Use at least 4 decimals.You must showm your calculation steps and brief explanation on your Excel spreadsheets.LINGO SOFTWARE Consider a production-mix problem where we are concerned with what mix of four products we should produce during the upcoming week. For each product, each unit produced requires a known amount of production time on each of the three machines. Each machine has a certain number of hours of production time available per week. Each product provides a certain profit per unit produced. Figure 3S1.2 shows three types of data: machine-related data, product-related data, and data related to combinations of a machine and product. The objective is to determine how much to produce for each product so that total profit is maximized while not exceeding the limited production capacity of each machine. Requirement: Solve this problem in LINGO software.TRUE OR FALSE In a simplex maximization slack variable is added to convert the objective function to equation.