Question

Problem 5-13 

A construction project is broken down into the following 10 activities:

b-1. What is the critical path? 

1-4-7-9-10 

1-3-6-9-10 

1-2-5-8-10 

1-3-5-8-10 

b-2. How many weeks will the project take to complete? 

Number of weeks _______ 

c. If activities 1 and 10 cannot be shortened, but activities 2 through 9 can be shortened to a minimum of one week each at a cost of $10,000 per week, which activities would you shorten to cut the project by four weeks? (You may select more than one answer. Single-click the box with the question mark to produce a checkmark for a correct answer and double-click the box with the question mark to empty the box for a wrong answer.) 

Cut activity 2 by 3 weeks. 

and then reduce activity 5 or 8 by one week. 

Cut activity 5 by 4 weeks. 

Reduce activities 5 and 8 by a total of 3 weeks. 

and then reduce activity 2 by one week.

Answer 1

Activity	Immediate Predecessor	Time (weeks)
1	-	2
2	1	4
3	1	2
4	1	2
5	2,3	5
6	3	6
7	4	1
8	5	5
9	6,7	4
10	8,9	5

The network diagram :

고 5 8 10 1 3 6 9 4 7

Possible paths and duration:

Path	Duration
1-2-5-8-10	2+4+5+5+5	21
1-3-5-8-10	2+2+5+5+5	19
1-3-6-9-10	2+2+6+4+5	19
1-4-7-9-10	2+2+1+4+5	14

b. 1-2-5-8-10 has the highest duration, so this is the critical path and project completion time is 21 weeks

c. 1,2,5,8,10 are critical activities so to reduce the project duration, the combination of the activities can be reduced.

Hence all options are correct.

Cut activities 2 by 3 weeks and then reduce activity 5 or 8 by 1 week

Cut activity 5 by 4 weeks

Cut activities 5 and 8 by a total of 3 weeks and then reduce 2 by a week.

Any of the above three options would reduce the project duration by 4 weeks as the project duration depends on the durations of the critical activities.