387,540.0
Hence, the total cost =
$826,596.0
(1 point)
Alternate solution
Labour hour
= 6,000(4.33921.9000) = 14,635.2
Materials, equipment usage and supplies = 200,000(3.73771.8000) = $387,540.
Question 3: (8 points)
Observed weekly sales of ball peen hammers at the town hardware store over a fiveweek period
have been 16, 12, 28, 24, 32.
a.
(3 points) Suppose that threeweek moving averages are used to forecast sales, Determine the
onestepahead forecasts for weeks 4 and 5.
67
18
3
28
12
16
4
.
=
+
+
=
F
33
21
3
24
28
12
5
.
=
+
+
=
F
b.
(3 points) Suppose that exponential smoothing is used to with a smoothing constant of
.
20
.
0
=
α
Find the exponential smoothing forecasts for weeks 4 and 5. (To get the method started, use the
same forecast for week 4 as you used in part
a
.)
67
18
4
.
=
F
(
29
736
19
67
18
24
20
0
67
18
5
.
.
.
.
=

+
=
F
c.
(2 points) Based on the MAD, which method did better?
8
2
33
21
32
67
18
24
=

+

=
.
.
MAD
MA
797
8
2
736
19
32
67
18
24
.
.
.
MAD
ES
=

+

=
Thus, moving average is better.
4
Name:_________________________________________________
ID:_________________________
Question 4: (10 points)
Lakeroad, a manufacturer of hard disks for personal computers, was founded in 2005 and has sold
the following number of disks:
Year
Numbers Sold (in 000s)
2005
24
2006
35
2007
47
a.
(7 points) Calculate the exponential smoothing with trend component forecast for years 2006 and
2007 using an initial trend forecast (
T
1
) of 12, an initial exponential smoothing forecast (
F
1
) of 13,
an
α
of 0.20, and a
δ
of 0.20.
Year
t
Actual
F
t
T
t
FIT
t
2005
24
13
12
13+12
= 25.00
2006
35
0.20(24)+0.80(25) = 24.80
(2 points)
0.20(24.8013)+0.80(12) = 11.96
(2 points)
24.80+11.96
= 36.76
(2 points)
2007
47
0.20(35)+0.80(36.76)
= 36.408
0.20(36.40824.80)+0.80(11.96)
= 11.89
36.408+11.89
= 48.298
(1 point)
b.
(3 points) What is the sales forecast for the year 2009 made at the end of 2007?
(
29
(
29
(
29
(
29
8266
71
89408
11
2
0384
48
89408
11
89
11
8
0
408
36
0384
48
20
0
0384
48
298
48
80
0
47
20
0
2009
2008
2008
2008
.
.
.
.
.
.
.
.
.
.
.
.
.
,
=
×
+
=
=
+

=
=
+
=
FIT
T
F
Question 5: (15 points)
Use regression analysis on deseasonalized demand to forecast demand in Fall 2007, given the
following historical demand data:
Year
Season
Actual
Demand
2005
Winter
61
Spring
77
Summer
79
Fall
64
2006
Winter
69
Spring
86
Summer
90
Fall
76
5
Name:_________________________________________________
ID:_________________________
Quarterly average demand = (61+77+79+64+69+86+90+76)/8 = 75.25
Season
Average demand
Seasonal Index
Winter
(61+69)/2 = 65.0
65.0/75.25 = 0.8640
Spring
(77+86)/2 = 81.5
81.5/75.25 = 1.0830
Summer
(79+90)/2 = 84.5
84.5/75.25 = 1.1230
Fall
(64+76)/2 = 70.0
70.0/75.25 = 0.9300
4.0000
Period
x
Demand
Deseasonalized
Demand
y
xy
2
y
1
61
70.6
70.6
1
2
77
71.1
142.2
4
3
79
70.4
211.1
9
4
64
68.8
275.2
16
5
69
79.9
399.4
25
6
86
79.4
476.4
36
7
90
80.1
561.0
49
8
76
81.7
653.6
64
∑
x
=36
∑
y
=602.0
∑
xy
=2789.5344
∑
2
y
=204
X
=4.5
Y
=75.25
(
29
(
29
(
29
(
29
(
29
9175
1
0
336
2752
644
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 EQUIPMENT USAGE, minimum constant workforce