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 activitys 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 and

>= 23 and

>= 26 and

> 29

Question 2

How much will this project cost (in $s) under normal conditions?

>= 300,000 and

>= 350,000 and

>= 400,000

Question 3

What would be the total cost of activity D if this activity is completed in 10 weeks?

>= 60,000 and

>= 70,000 and

>= 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 I G