Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 13.3, Problem 9P
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To determine: The MAPE for the power trendline.
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Cell phone sales for a California-based firm over the last 10 weeks are shown in the following table. Plot the data, and visually check to see if a linear trend line would be appropriate.Then determine the equation of the trend line, and predict sales for weeks 11 and 12.Week Unit Sales1 7002 7243 7204 7285 7406 7427 7588 7509 77010 775
Please help with correct answers in details: Step by step
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.
Week
Sales (1,000sof gallons)
1
17
2
21
3
20
4
24
5
18
6
17
7
21
8
19
9
22
10
21
11
16
12
22
(a)
Compute four-week and five-week moving averages for the time series.
Week
Time SeriesValue
4-WeekMovingAverageForecast
5-WeekMovingAverageForecast
1
17
2
21
3
20
4
24
5
18
6
17
7
21
8
19
9
22
10
21
11
16
12
22
b) Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)
c) Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)
d) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? MSE for the three-week moving average is 9.65.…
Use Excel to make calculations
Given the following sales data:
Quarter
Year 1
Year 2
1
120
150
2
160
200
3
210
250
4
130
170
Compute the seasonal index for each quarter and forecast quarterly demand for year 3 with a projected annual demand of 1000.
The efficiency of a production unit is 70 percent. The unit produces an average of 100 products per day. Determine the effective capacity of the unit.
The utilization of a machine is 60 percent. The machine has a design capacity of 150 units per hour and an effective capacity of 100 units per hour. Find the efficiency of the machine.
FloorsRUs is considering new locations for its manufacturing plants. Costs for constructing a new facility in Huntsville are $1,100,000 and the company estimates that for every product from its new line, there would be an additional cost of $3. If the company were to locate in Hays, the new facility would cost $1,800,000 and each product would incur a $2…
Chapter 13 Solutions
Practical Management Science
Ch. 13.3 - The file P13_01.xlsx contains the monthly number...Ch. 13.3 - The file P13_02.xlsx contains five years of...Ch. 13.3 - The file P13_03.xlsx contains monthly data on...Ch. 13.3 - The file P13_04.xlsx lists the monthly sales for a...Ch. 13.3 - Management of a home appliance store wants to...Ch. 13.3 - Do the sales prices of houses in a given community...Ch. 13.3 - Prob. 7PCh. 13.3 - The management of a technology company is trying...Ch. 13.3 - Prob. 9PCh. 13.3 - Sometimes curvature in a scatterplot can be fit...
Ch. 13.4 - Prob. 12PCh. 13.4 - A trucking company wants to predict the yearly...Ch. 13.4 - An antique collector believes that the price...Ch. 13.4 - Stock market analysts are continually looking for...Ch. 13.4 - Suppose that a regional express delivery service...Ch. 13.4 - The owner of a restaurant in Bloomington, Indiana,...Ch. 13.6 - The file P13_19.xlsx contains the weekly sales of...Ch. 13.6 - The file P13_20.xlsx contains the monthly sales of...Ch. 13.6 - The file P13_21.xlsx contains the weekly sales of...Ch. 13.6 - The file P13_22.xlsx contains total monthly U.S....Ch. 13.7 - You have been assigned to forecast the number of...Ch. 13.7 - Simple exponential smoothing with = 0.3 is being...Ch. 13.7 - The file P13_25.xlsx contains the quarterly...Ch. 13.7 - The file P13_26.xlsx contains the monthly number...Ch. 13.7 - The file P13_27.xlsx contains yearly data on the...Ch. 13.7 - The file P13_28.xlsx contains monthly retail sales...Ch. 13.7 - The file P13_29.xlsx contains monthly time series...Ch. 13.7 - A version of simple exponential smoothing can be...Ch. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Management of a home appliance store would like to...Ch. 13 - A small computer chip manufacturer wants to...Ch. 13 - The file P13_35.xlsx contains the amount of money...Ch. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 39PCh. 13 - The Baker Company wants to develop a budget to...Ch. 13 - Prob. 41PCh. 13 - The file P13_42.xlsx contains monthly data on...Ch. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 49P
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- Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the previous problem. Still another fairly simple trend line is the parabola, a polynomial of order 2 (also called a quadratic). For the demand-price data in the file P13_10.xlsx, fit all three of these types of trend lines to the data, and calculate the MAPE for each. Which provides the best fit? (Hint: Note that a polynomial of order 2 is still another of Excels Trend line options.)arrow_forwardA company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?arrow_forwardPlay Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.arrow_forward
- An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.arrow_forwardThe Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?arrow_forwardYou are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)arrow_forward
- Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.arrow_forwardSuppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.arrow_forwardStock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for 16 electric utility stocks are provided in the file P13_15.xlsx. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.arrow_forward
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