5/25/2018 BUSII411 HW 1- Ch 3

1/9

Problem 3-2

National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month

eriod were as follows:

Month

Sales

(000)Units

Feb. 15

Mar. 20

Apr. 14

May. 24

Jun. 18

Jul. 20

Aug. 30

. Forecast September sales volume using each of the following:

(1) A linear trend equation.(Round your intermediate calculations and final answer to 2

decimal places.)

Yt 27.14 thousands

(2) A five-month moving average. (Round your answer to 2 decimal places.)

Moving average 21.20 thousands

(3) Exponential smoothing with a smoothing constant equal to .40, assuming a March

forecast of 17(000).(Round your intermediate calculations and final answer to 2

decimal places.)

5/25/2018 BUSII411 HW 1- Ch 3

2/9

Forecast 23.61 thousands

(4) The naive approach.

Naive approach30 \ thousands

(5) A weighted average using .60 for August, .10 for July, and .30 for Jun e.(Round

your answer to 2 decimal places.)

Weighted

average25.40 thousands

rev: 03_15_2012, 05_23_2013_QC_30974

Explanation:

b.

(1)

t y ty

1 15 15

2 20 40

3 14 42

4 24 96

5 18 90

6 20 120

7 30 210

28 141 613

5/25/2018 BUSII411 HW 1- Ch 3

3/9

ith n= 7, t= 28, t2= 140

b =

nty ty

=

7(613) 28(141)

= 1.75

nt2 (t)

2 7(140) 28(28)

a =

y bt

=

141 1.75(28)

= 13.14

n 7

For Sept., t= 8, and Yt= 13.14 + 1.75(8) = 27.14

(000)

(2)

MA5=

14 + 24 + 18 + 20 + 30

= 21.205

(3)

Month Forecast = F( old ) +.40[Actual F(Old)]

April 18.20 = 17.00 +.40 [20 17.00]

May 16.52 = 18.20 +.40 [14 18.20]

June 19.51 = 16.52 +.40 [24 16.52]

July 18.91 = 19.51 +.40 [18 19.51]

August 19.35 = 18.91 +.40 [20 18.91]

September 23.61 = 19.35 +.40 [30 19.35]

(5)

5/25/2018 BUSII411 HW 1- Ch 3

4/9

.60(30) + .10(20) + .30(18) = 25.40

Problem 3-7

Freight car loadings over an 18-week period at a busy port are as follows:

Week Number Week Number Week Number

1 220 7 350 13 461

2 245 8 360 14 475

3 277 9 404 15 502

4 275 10 380 16 510

5 340 11 441 17 543

6 310 12 450 18 541

a. Determine a linear trend line for expected freight car loadings. (Round your

intermediate calculations and final answers to 3 decimal places.)

= 212.732 + 19.034 t

. Use the trend equation to predict expected loadings for weeks 22 and 23. (Round your

intermediate calculations and final answers to 3 decimal places.)

The forecasted demand for week 22 and 23 is 631.481 and 650.515 respectively.

c. The manager intends to install new equipment when the volume exceeds 829 loadings

er week. Assuming the current trend continues, the loading volume will reach that

level in approximately how many more weeks? (Round your intermediate calculations

to 3 decimal places and final answer to the nearest whole number.)

It would take approximately 15 more weeks.

5/25/2018 BUSII411 HW 1- Ch 3

5/9

rev: 02_25_2012, 03_15_2012, 01_31_2013_QC_25862, 09_05_2013_QC_34423

Explanation:

a.

t y t*y t2

1 220 220 1

2 245 490 4

3 277 831 9

4 275 1,100 16

5 340 1,700 25

6 310 1,860 36

7 350 2,450 49

8 360 2,880 64

9 404 3,636 81

10 380 3,800 100

11 441 4,851 121

12 450 5,400 144

13 461 5,993 169

14 475 6,650 196

15 502 7,530 225

16 510 8,160 256

17 543 9,231 289

18 541 9,738 324

171 7,084 76,520 2109

5/25/2018 BUSII411 HW 1- Ch 3

6/9

ti=171 yi= 7,084

ti2= 2109 tiyi=76,520

b =

(n)(tiyi) (ti)(yi)

(n)(ti2) (ti)

2

b =

(18)(76,520) (171)(7,084)

=

165,996

= 19.034

(18)(2109) (171)2 8,721

a =

y bt

or

n

a =

7,084 19.034(171)

18

a =

3,829.186=

212.73318

b.

F =212.733 +(19.034)(22) = 631.481

F =212.733 +(19.034)(23) = 650.515

The forecasted demand for week 22 and 23 is 631.481 and 650.515 respectively.

5/25/2018 BUSII411 HW 1- Ch 3

7/9

c.

829 541

= 15.13 Weeks

19.034

It would take approximately 15 more weeks. Since we have just completed week 18, the

loading volume is expected to reach 829 by week 33 (18 + 15).

Problem 3-13

The manager of a fashionable restaurant open Wednesday through Saturday says that the

restaurant does about 35 percent of its business on Friday night, 35 percent on Saturday

night, and 18 percent on Thursday night. What seasonal relatives would describe this

situation?(Round your answers to 2 decimal places.)

Wednesday 0.48

Thursday 0.72

Friday 1.40

Saturday 1.40

Explanation:

Wednesday=.12 4 = .48

Thursday =.18 4 = .72

Friday =.35 4 = 1.40

Saturday =.35 4 = 1.40

rev: 03_15_2012

Problem 3-20

An analyst must decide between two different forecasting techniques for weekly sales of

5/25/2018 BUSII411 HW 1- Ch 3

8/9

roller blades: a linear trend equation and the naive approach. The linear trend equation is

Ft= 124 + 2.1t, and it was developed using data from periods 1 through 10. Based on data

for periods 11 through 20 as shown in the table, which of these two methods has the

greater accuracy if MAD and MSE are used? (Round your answers to 2 decimal places.)

t Units Sold

11 144

12 146

13 152

14 142

15 152

16 149

17 152

18 154

19 157

20 164

MAD (Naive) 5.11

MAD

(Linear)5.47

MSE (Naive) 22.97

MSE (Linear)40.83

Naive method provides forecasts with less average error and less average squared

error.

rev: 03_15_2012, 01_04_2013

5/25/2018 BUSII411 HW 1- Ch 3

9/9