Answer Happy

Activity
Normal Duration (weeks)
Minimum Duration
(weeks)
Normal Cost ($)
Maximum Cost ($)
A
10
8
50,000
62,000
B
5
4
25,000
32,000
C
4
3
20,000
28,000
D
12
8
60,000
90,000
E
15
13
75,000
92,000
F
6
4
30,000
42,000
G
8
5
40,000
62,500
H
7
6
35,000
44,500
LP Formulation
Decision variables
FA = finish time of activity A
FB = finish time for activity B
FC = finish time for activity C
FD = finish time for activity D
FE = finish time for activity E
FF = finish time for activity F
FG = finish time for activity G
FH = finish time for activity H
SA = start time of activity A
SB = start time of activity B
SC = start time of activity C
SD = start time of activity D
SE = start time of activity E
SF = start time of activity F
SG = start time of activity G
SH = start time of activity H
E0 = event time of event 0
= project start time
E1 = event time of event 1
E2 = event time of event 2
E3 = event time of event 3
E4 = event time of event 4
E5 = event time of event 5
E6 = event time of event 6
= desired project completion time
TA = crash time of activity A
TB = crash time of activity B
TC = crash time of activity C
TD = crash time of activity D
TE = crash time of activity E
TF = crash time of activity F
TG = crash time of activity G
TH = crash time of activity H
Note: The crash time for an activity is the amount of time
subtracted from the activity’s normal duration
Parameters
DA = normal duration of activity A
DB = normal duration of activity B
DC = normal duration of activity C
DD = normal duration of activity D
DE = normal duration of activity E
DF = normal duration of activity F
DG = normal duration of activity G
DH = normal duration of activity H
Question 1
What is the shortest possible completion time (in weeks) for
this project?
< 20
>= 20 and < 23
>= 23 and < 26
>= 26 and < 29
> 29
Question 2
How much will this project cost (in $’s)
under normal conditions?
< 300,000
>= 300,000 and < 350,000
>= 350,000 and < 400,000
>= 400,000
Question 3
What would be the total
cost of
activity D if this activity is
completed in 10 weeks?
< 60,000
>= 60,000 and < 70,000
>= 70,000 and < 80,000
>= 80,000
Question 4
What is the cheapest way to reduce the duration of the project
by one week from its normal duration?
Reduce activity A by one week
Reduce activity B by one week
Reduce activity C by one week
Reduce activity D by one week
Reduce activity E by one week
Reduce activity F by one week
Reduce activity G by one week
Reduce activity H by one week
Question 5
Which of the following expressions is the objective for this
crashing problem?
Minimize 6,000 DA + 7,000 DB + 8,000 DC + 7,500 DD + 8,500 DE +
6,000 DF + 7,500 DG + 9,500 DH
Minimize 62,000 TA + 32,000 TB + 28,000 TC + 90,000 TD + 92,000
TE + 42,000 TF + 62,500 TG + 44,500 TH
Minimize 6,000 FA + 7,000 FB + 8,000 FC + 7,500 FD + 8,500 FE +
6,000 FF + 7,500 FG + 9,500 FH
Minimize 6,000 TA + 7,000 TB + 8,000 TC + 7,500 TD + 8,500 TE +
6,000 TF + 7,500 TG + 9,500 TH
Question 6
Which of the following expressions would be included as a
constraint in a linear programming formulation of the crashing
problem for the project?
FB=SB-DB+TB
DE>=0
E3>=FD
TE>=2
4 B P ш п ол I І G