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The US government has contracted with Raytheon to build its new Peacekeeper 2 ballistic missile. The project has been laid out with durations (in weeks), predecessors, and costs included:   Activity     Normal Time (weeks)     Crashed Time (weeks)     Normal Cost     Crashed Cost     Predecessor(s)  A 3 2 $2,200 $2,900 -B 7 5 $1,200 $1,340 -C 7 4 $1,100 $1,700 AD 4 3 $2,150 $3,120 AE 4 3 $650 $800 BF 3 2 $530 $730 EG 9 6 $475 $670 D, CWhich of the following is the critical path?   A-D-G B-E-F A-C-GIf you wanted to shorten the duration of the project, which activity would you crash first? C E G BWhat is the weekly crashing cost of the activity selected in the previous question? (Display your answer to two decimal places.)     Crash the project from 19 weeks to 14 weeks. What is the total cost of crashing the project (just the additional cost, not total project cost)? (Display your answer to two decimal places.)

Question

The US government has contracted with Raytheon to build its new Peacekeeper 2 ballistic missile. The project has been laid out with durations (in weeks), predecessors, and costs included:   Activity     Normal Time (weeks)     Crashed Time (weeks)     Normal Cost     Crashed Cost     Predecessor(s)  A 3 2 2,2002,200 2,900 -B 7 5 1,2001,200 1,340 -C 7 4 1,1001,100 1,700 AD 4 3 2,1502,150 3,120 AE 4 3 650650 800 BF 3 2 530530 730 EG 9 6 475475 670 D, CWhich of the following is the critical path?   A-D-G B-E-F A-C-GIf you wanted to shorten the duration of the project, which activity would you crash first? C E G BWhat is the weekly crashing cost of the activity selected in the previous question? (Display your answer to two decimal places.)     Crash the project from 19 weeks to 14 weeks. What is the total cost of crashing the project (just the additional cost, not total project cost)? (Display your answer to two decimal places.)

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Solution

To answer these questions, we first need to determine the critical path. The critical path is the sequence of activities with the longest duration. A delay in these activities will delay the entire project.

  1. Critical Path:
    • Path A-D-G: 3 weeks (A) + 4 weeks (D) + 9 weeks (G) = 16 weeks
    • Path B-E-F: 7 weeks (B) + 4 weeks (E) + 3 weeks (F) = 14 weeks
    • Path A-C-G: 3 weeks (A) + 7 weeks (C) + 9 weeks (G) = 19 weeks

So, the critical path is A-C-G.

  1. To shorten the duration of the project, we would crash the activity on the critical path that has the lowest crashing cost per week. The crashing cost per week is calculated as (Crashed Cost - Normal Cost) / (Normal Time - Crashed Time).

    • Activity A: (2900−2900 - 2200) / (3 - 2) = $700 per week
    • Activity C: (1700−1700 - 1100) / (7 - 4) = $200 per week
    • Activity G: (670−670 - 475) / (9 - 6) = $65 per week

So, we would crash activity G first.

  1. The weekly crashing cost of activity G is $65.

  2. To crash the project from 19 weeks to 14 weeks, we need to reduce 5 weeks. We start with the activity with the lowest crashing cost per week, which is G. But we can only crash G by 3 weeks, so we need to crash another activity by 2 weeks. The next lowest cost is C.

    • The cost to crash G by 3 weeks is 3 weeks * 65/week=65/week = 195.
    • The cost to crash C by 2 weeks is 2 weeks * 200/week=200/week = 400.

So, the total cost of crashing the project is 195+195 + 400 = $595.

This problem has been solved

Similar Questions

The US government has recently contracted with Boeing to build its fleet of airborne tankers. The project has been laid out with durations (in weeks), predecessors, and costs included:    Activity     Normal Time (weeks)     Crashed Time (weeks)     Normal Cost     Crashed Cost     Predecessor(s)  A 8 5 $1,550 $1,950 -B 8 7 $1,400 $2,450 -C 10 8 $950 $2,350 BD 5 4 $2,300 $2,800 AE 4 3 $660 $1,050 BF 3 2 $600 $1,150 EG 10 6 $440 $1,120 C, D, F What is the critical path of the project? A-D-G B-C-G B-E-F-G If you wanted to shorten the overall duration of the project, which activity would you crash first?  B G C E What would be the weekly crashing cost of the activity you selected in the previous question? (Display your answer to two decimal places.)     Crash the project by 5 weeks. What is the total cost of crashing the project (just the additional cost, not total project cost)? (Display your answer to two decimal places.)

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