# MAT540

MAT540

Week 4 Homework

Chapter 15

1.      The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customer  will  buy  their  carpet  from  one  of  Carpet  City’s  many  competitors.  The  manager  has

collected the following demand data for the past 8 months:

Month

Demand for Soft Shag

Carpet (1,000 yd.)

1                                                   10

2                                                    9

3                                                    8

4                                                    9

5                                                   10

6                                                   12

7                                                   14

8                                                   11

a.    Compute a 3-month moving average forecast for months 4 through 9.

b.    Compute  a  weighted  3-month  moving  average  forecast  for  months  4  through  9.  Assign weights  of  0.55, 0.35, and 0.10 to the  months in sequence, starting with  the  most  recent month.

c.    Compare the two forecasts by using MAD. Which forecast appears to be more accurate?

2.      The  manager  of  the  Petroco  Service  Station  wants  to forecast  the  demand  for  unleaded  gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated  the  following  data  on  demand  for  unleaded  gasoline  from  sales  during  the  past  10 months:

Month                                       Gasoline Demanded (gal.) October                                                        775

November                                                    835

December                                                    605

January                                                       450

February                                                     600

March                                                          700

April                                                             820

May                                                              925

June

July

1500

1200

a.    Compute an exponential smoothed forecast, using an α value of 0.4

3.      Emily  Andrews  has  invested  in  a  science  and  technology  mutual  fund.  Now  she  is  considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during the past 20 months:

Month                                        Fund Price

1                                                \$55 ¾

2                                                 54 ¼

3                                                55 1/8

4                                                58 1/8

5                                                53 3/8

6                                                51 1/8

7                                                 56 ¼

8                                                59 5/8

9                                                 62 ¼

10                                                59 ¼

11                                               62 3/8

12                                               57 1/1

13                                               58 1/8

14                                                62 ¾

15                                                64 ¾

16                                               66 1/8

17                                                68 ¾

18                                                60.5

19                                              65.875

20                                               72.25

a.    Using a 3-month average, forecast the fund price for month 21.

b.    Using a 3-month weighted average with the most recent month weighted 0.5, the next most recent month weighted 0.30, and the third month weighted 0.20, forecast the fund price for month 21.

c.   Compute an exponentially smoothed forecast, using α=0.3, and forecast the fund price for month 21.

d.    Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.

4.      Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store’s sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records

on monthly sales. These data are as follows:

Monthly Carpet Sales

(1,000 yd.)

Monthly Construction

Permits

9                                                                     17

14                                                                   25

10                                                                    8

12                                                                    7

15                                                                   14

9                                                                      7

24                                                                   45

21                                                                   19

20                                                                   28

29                                                                   28

a.   Develop  a linear  regression  model  for these  data and  forecast  carpet  sales if 30  construction permits for new homes are filed.

b.    Determine  the  strength  of  the  causal  relationship  between  monthly  sales  and  new  home construction by using correlation.

5.       The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice cream.

The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and  if  it  orders too  much,  the  extra  must  be  thrown away.  The  manager  belives that  a major determinant of ice cream sales is temperature (i.e.,the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average day time temperature for

14 weeks, selected at random, and from store records he has determined the ice cream consumption

for the same 14 weeks. These data are summarized as follows:

Week

Average Temperature

(Degrees)

Ice Cream Sold

(gal.)

1                                            68                                                80

2                                            70                                               115

3                                            73                                                91

4                                            79                                                87

5                                            77                                               110

6                                            82                                               128

7                                            85                                               164

8                                            90                                               178

9                                            85                                               144

10                                           92                                               179

11                                           90                                               144

12                                           95                                               197

13                                           80                                               144

14                                           75                                               123

a.   Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees.

b.    Determine   the   strength   of   the   linear   relationship   between   temperature   and   ice   cream consumption by using correlation.

c.    What is the coefficient of determination? Explain its meaning.

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