The Department of Transportation has found that a proposed highway project is no
ID: 451237 • Letter: T
Question
The Department of Transportation has found that a proposed highway project is not going to be completed before the end of the summer. They have asked the contractor to prepare cost figures to shorten the project by up to 6 weeks.
The following table shows the Crashing Costs for each activity. For example, if you needed to shorten Activity 1-2 by 1 week this would cost $12. If you needed to shorten the same activity by 2 weeks it would cost $16. Note: If an activity lists a cost of $---, then this activity cannot be any shorter.
Activity
First Week
Second Week
Third Week
1-2
$12
$16
$ ---
2-5
6
8
10
5-7
7
8
11
7-11
7
11
---
11-13
4
8
10
1-3
12
14
19
3-8
5
---
---
8-11
12
13
14
3-9
14
16
16
9-12
8
8
10
12-13
7
11
---
1-4
10
14
18
4-6
12
14
18
6-10
11
12
---
10-12
14
15
---
Currently the Length of the Project is
weeks.
Determine the costs to shorten the project.
1st Week Cost =
Hint: Between 1 and 5
2nd Week Cost =
3rd Week Cost =
4th Week Cost =
Hint: Between 17 and 20
5th Week Cost =
6th Week Cost =
Activity
First Week
Second Week
Third Week
1-2
$12
$16
$ ---
2-5
6
8
10
5-7
7
8
11
7-11
7
11
---
11-13
4
8
10
1-3
12
14
19
3-8
5
---
---
8-11
12
13
14
3-9
14
16
16
9-12
8
8
10
12-13
7
11
---
1-4
10
14
18
4-6
12
14
18
6-10
11
12
---
10-12
14
15
---
Explanation / Answer
Answer: The paths are:
1-2-5-7-11-13 = 34 weeks
1-3-8-11-13 = 35
1-3-9-12-13 = 34
1-4-6-10-12-13 = 32
so the critical path is 1-3-8-11-13 and the completition time is 35 weeks which is also the length of the project.
Now cost to short time by 1 week between 1-5 = $12 + $6 = $18
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