We also put the condition that
T
and
A
should be integer.
– First constraint represent funds available. (in
1000s)
– Second constraint represents managers time.
– Third constraint represents Townhouse available.
The
optimal
solution
is
(2.479,3.252).
The
value
of
the objective function is con-
stant along the line
10
T
+ 15
A
=
c
and
it
increases
for
the
lines
away from the origin.
The op-
timal solution lies along the line
10
T
+ 15
A
= 73
.
574
The maximum value of the ob-
jective function is 73.574.
However, we are interested in integer solution.
Rounding the solution to (2,3) gives the
objective function value 65, which is less than the non-integer solution. However, we are
not sure that this is the optimal integer solution.
Rcode/QM shows that the solution is (4,2) and the optimal solution is 70.

31

3
1
st
Week Learning Activity
Problem 3.0.1
Consider the following time series data:
Week
1
2
3
4
5
6
Value
18
13
16
11
17
14
Compute three week moving average forecast and forecast using exponential smoothing (
α
=
0
.
02).
Problem 3.0.2
Consider the following time series data:
32

BUSI 2013
FALL 2020
Week
1
2
3
4
5
6
Value
18
13
16
11
17
14
You computed three week moving average forecast and forecast using exponential smoothing
(
α
= 0
.
02) in the previous learning activity. Compute mean absolute error and mean square
error for these methods.
33

4
2
nd
Week Learning Activity
Problem 4.0.1
Data given here provides information on the
amount of gasoline sold per week. Find the
regression equation for the linear trend com-
ponent for the gasoline sales time series.
after signing the new contract. Figure 6.2 shows the correspondi
the increased level of the time series beginning in week 13. This
time series makes it more difficult to choose an appropriate forec
a forecasting method that adapts well to changes in the level of
tant consideration in many practical applications.
Trend Pattern
Although time series data generally exhibit random fluctuation
show gradual shifts or movements to relatively higher or lower va
192
Chapter 6
Time Series Analysis and Forecasting
Week
Sales (1000s of gallons)
Week
Sa
1
17
12
2
21
13
3
19
14
4
23
15
5
18
16
6
16
17
7
20
18
8
18
19
9
22
20
10
20
21
11
15
22
TABLE 6.2
GASOLINE SALES TIME SERIES AFTER OBTAINING T
THE VERMONT STATE POLICE
file
WEB
Gasoline Revised
10
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19
40
35
30
20
5
25
15
Sales (1000s of gallons)
Week
FIGURE 6.2
GASOLINE SALES TIME SERIES PLOT AFTER OBTAIN
WITH THE VERMONT STATE POLICE
62345_06_ch06_p188-244.qxd
12/22/11
2:39 PM
Page 192
34

BUSI 2013
FALL 2020
Problem 4.0.2
A financial advisor at Baroda Investments identified two companies that are
likely candidates for a takeover in the near future. Eastern cable is a leading manufacturer
of flexible cable systems used in the construction industry, and comswitch is the new firm
specializing in digital switching systems.
Eastern cable is currently trading for
40 per
share, and comswitch is currently trading for
25 per share.
If the takeovers occur, the
financial advisor estimates that the price of eastern cable will go to
55 per share and
comswitch will go to
43 per share. At this point in time, the financial advisor has identified