Download - BUSII411 HW 1- Ch 3
Problem 3-2
National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:
MonthSales(000)Units
Feb. 15
Mar. 20
Apr. 14
May. 24
Jun. 18
Jul. 20
Aug. 30
b. 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.)
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 average
25.40 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
with n = 7, Σt = 28, Σt2 = 140
b =
nΣty − ΣtΣy
=
7(613) − 28(141)
= 1.75
nΣt2 − (Σt)2 7(140) − 28(28)
a =
Σy − bΣt
=
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
= 21.20
5
(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)
.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
b. 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 per 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.
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
Σti = 171 Σyi = 7,084
Σti2 = 2109 Σtiyi = 76,520
b =
(n)(Σtiyi) − (Σti)(Σyi)
(n)(Σti2) − (Σti)2
b =
(18)(76,520) − (171)(7,084)
=
165,996
= 19.034
(18)(2109) − (171)2 8,721
a =
Σy − bΣt
or
n
a =
7,084 − 19.034(171)
18
a =
3,829.186= 212.733
18
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.
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 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