Essentials of Business Analytics (MindTap Course List)
Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN: 9781305627734
Author: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher: Cengage Learning
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Chapter 8, Problem 27P

Hogs & Dawgs is an ice cream parlor on the border of north-central Louisiana and southern Arkansas that serves 43 flavors of ice creams, sherbets, frozen yogurts, and sorbets. During the summer Hogs & Dawgs is open from 1:00 p.m. to 10:00 p.m. on Monday through Saturday, and the owner believes that sales change systematically from hour to hour throughout the day. She also believes her sales increase as the outdoor temperature increases. Hourly sales and the outside temperature at the start of each hour for the last week are provided in the file IceCreamSales.

  1. a. Construct a time series plot of hourly sales and a scatter plot of outdoor temperature and hourly sales. What types of relationships exist in the data?
  2. b. Use a simple regression model with outside temperature as the causal variable to develop an equation to account for the relationship between outside temperature and hourly sales in the data. Based on this model, compute an estimate of hourly sales for today from 2:00 p.m. to 3:00 p.m. if the temperature at 2:00 p.m. is 93°F.
  3. c. Use a multiple linear regression model with the causal variable outside temperature and dummy variables as follows to develop an equation to account for both seasonal effects and the relationship between outside temperature and hourly sales in the data in the data:

Hour1 = 1 if the sales were recorded between 1:00 p.m. and 2:00 p.m., 0 otherwise;

Hour2 = 1 if the sales were recorded between 2:00 p.m. and 3:00 p.m., 0 otherwise;

M

Hour8 = 1 if the sales were recorded between 8:00 p.m. and 9:00 p.m., 0 otherwise.

Note that when the values of the 8 dummy variables are equal to 0, the observation corresponds to the 9:00-to-l0:00-p.m. hour.

Based on this model, compute an estimate of hourly sales for today from 2:00 p.m. to 3:00 p.m. if the temperature at 2:00 p.m. is 93°F.

  1. d. Is the model you developed in part (b) or the model you developed in part (c) more effective? Justify your answer.
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The owner of an apartment building can rent all 50 apartments if she charges $1,700 per month, but she rents one fewer apartment for each $50 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $1,700, $1,750, and $1,800. Total Revenue No. of Apts 50 49 48 Rent $1,700 $ 85000 $1,750 $ 85750 $1,800 $ 86400 Need Help? ✓ Excellent job! (b) Does her revenue from apartment rentals increase or decrease as she increases the rent from $1,700 to $1,800? o revenue increases revenue decreases Read It ✓ Great job. ✓ Way to go! Nice work. (c) Write an equation that gives the revenue R, from apartment rentals if she makes x increases of $50 in the rent. R(x) = -50x² +800x+8500 X (d) Find the rent she should charge to maximize her revenue. $2100 ✓per month
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Essentials of Business Analytics (MindTap Course List)

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