SOLUTION – ASSIGNED PROBLEMS – CHAPTER 12
1.
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5.
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7. a.
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b. A-D-E-H
c. Activity F: 4 weeks
d. Yes, project completion time is 16 weeks
| |Earliest |Latest |Earliest |Latest | |Critical |
|Activity |Start |Start |Finish |Finish |Slack |Activity |
|A |0 |0 |3 |3 |0 |Yes |
|B |0 |2 |1 |3 |2 | |
|C |0 |1 |2 |3 |1 | |
|D |3 |3 |7 |7 |0 |Yes |
|E |7 |7 |12 |12 |0 |Yes |
|F |3 |7 |6 |10 |4 | |
|G |7 |10 |13 |16 |3 | |
|H |12 |12 |16 |16 |0 |Yes |
9. a. A-C-E-H-I
b.
| |Earliest |Latest |Earliest |Latest | |Critical |
|Activity |Start |Start |Finish |Finish |Slack |Activity |
|A | 0 | 0 | 9 | 9 |0 |Yes |
|B | 0 | 9 | 6 |15 |9 | |
|C | 9 | 9 |15 |15 |0 |Yes |
|D | 9 |12 |12 |15 |3 | |
|E |15 |15 |15 |15 |0 |Yes |
|F |15 |16 |18 |19 |1 | |
|G |18 |19 |20 |21 |1 | |
|H |15 |15 |21 |21 |0 |Yes |
|I |21 |21 |24 |24 |0 |Yes |
c. Project completion 24 weeks. The park can open within the 6 months (26 weeks) after the project is started.
11.
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20. a.
| |Maximum |Crash |
|Activity |Crash |Cost/Week |
|A |2 | 400 |
|B |3 | 667 |
|C |1 | 500 |
|D |2 | 300 |
|E |1 | 350 |
|F |2 | 450 |
|G |5 | 360 |
|H |1 |1000 |
|Min |400YA |+ |667YB |
|xB + yB ≥ 6 |xF + yF - xE ≥ 3 |xH |≤ 16 |
|xC + yC - xA ≥ 2 |xG + yG - xC ≥ 9 | | |
|xD + yD - xC ≥ 5 |xG + yG - xB ≥ 9 | | |
|xD + yD - xB ≥ 5 |xH + yH - xF ≥ 3 | | |
Maximum Crashing: yA ≤ 2 yB ≤ 3 yC ≤ 1 yD ≤ 2 yE ≤ 1 yF ≤ 2 yG ≤ 5 yH ≤ 1
b. Linear Programming Solution
|Activity |Crash Time |New Time |Crash Cost |
|A |0 |3 | — |
|B |1 |5 | 667 |
|C |0 |2 | — |
|D |2 |3 | 600 |
|E |1 |3 | 350 |
|F |1 |2 | 450 |
|G |1 |8 | 360 |
|H |0 |3 | — |
| | |Total Crashing Cost |$2,427 |
c.
| |Earliest |Latest |Earliest |Latest | |Critical |
|Activity |Start |Start |Finish |Finish |Slack |Activity |
|A | 0 | 0 | 3 | 3 |0 |Yes |
|B | 0 | 0 | 5 | 5 |0 |Yes |
|C | 3 | 3 | 5 | 5 |0 |Yes |
|D | 5 | 5 | 8 | 8 |0 |Yes |
|E | 8 | 8 |11 |11 |0 |Yes |
|F |11 |11 |13 |13 |0 |Yes |
|G | 5 | 5 |13 |13 |0 |Yes |
|H |13 |13 |16 |16 |0 |Yes |
All activities are critical.
22. a.
| | |Crash |
|Activity |Max Crash Days |Cost/Day |
|A |1 |600 |
|B |1 |700 |
|C |2 |400 |
|D |2 |400 |
|E |2 |500 |
|F |1 |400 |
|G |1 |500 |
|Min |600yA |+ |
|C |1 day |$400 |
|E |1 day | 500 |
| |Total |$900 |
c. Total Cost = Normal Cost + Crashing Cost = $8,400 + $900 = $9,300
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Finish
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