Question

For the following precedence relationship, answer questions 5 thru 9. Activity Preceding Activity Optimistic Time (weeks) 10 Most Likely Time (weeks) 222 Pessimistic Time (weeks) A CD 5. The project duration for the above project is: a 25 weeks b. 30 weeks c. 40 weeks d. 38 weeks 6. The slack for activity Cis: a. O weeks b. 3 weeks C 5 weeks d. 7 weeks 7. The critical path for the above project is: a. ACHEG b. A-D-E-G C. A-C-F-G and A-B-D-F-G d. AC EG and A-B-D-E-G 8. The probability of finishing the above project in 35 weeks or less is a 17% b. 19.22% C 24.35% d. 34.48% 9. The slack for activity is a. 3 weeks b. 2 weeks c. 5 weeks d. Oweeks

Answer 1

First, we need to calculate the mean time for the activities. Following formula can be used to calculate the mean time

= (t +4, +) where. t = Mean Time to = Optimistic Time t = Most Likely Time t = Pessimistic Time

Activity Optimistic Time Most Likely time Pessimistic time Mean Time N CUI NON MOON N CONNU

The precedence relationship diagram is as follows:

ED=28 Lo=28 EF=36 LE = 36 EA = 21 LA =21 B Dit Ea=38 pha=38 A = 28 tc=28 28 JE Eq=33 Lq=36 Critical paths is A - B - Daf - G And A-C- F - G

As per the network diagram:

5. The project duration for the above project is 38 weeks

6. The slack for activity C is 0 weeks because this activity comes on the critical path.

7. The critical path for the above projects are:

a) A-B-D-F-G

b) A-C-F-G

8. Following formula can be used to calculate the probability in less than 35 weeks

$1586906610745_image.png$

where,

Ts = Target Value

Te = Mean completion time

o = Standard Deviation

To calculate the standard deviation, first variance needs to be calculated for critical path.

$1586906771661_image.png$

Activity Optimistic Time Most Likely time Pessimistic time Mean Time Variance NC UNAN NEW 7 2.777778 2 0.111111 5 1.777778 8 0.111111 0 14.77778 Total

o = Sum of Critical path Variances o = 11.889 o=3.44

DZI.-I, 35-38 = Prob.{Z S-0.8720}=0.1916 o 3.44

Therefore, the probability of finishing the project in less than 35 weeks is 19.22 percent

9. By referring the precedence network diagram:

The slack for activity E is 36-33 = 3 weeks

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