At a local university, the Student Commission on Programming and Entertainment (

Question

At a local university, the Student Commission on Programming and Entertainment (SCOPE) is preparing to host its first rock concert of the school year. To successfully produce this rock concert, SCOPE has listed the requisite activities and related information in the following table (duration estimates measured in days). a. Draw the project network. b. Compute the expected duration and variance of each activity. c. Determine the critical path in the project network. d. What is the expected duration and variance of the critical path? e. What is the likelihood that the project will be completed within 30 days? f. If activity B is delayed by six days beyond its early start time, how does this affect the expected project duration?

Explanation / Answer

Correct project network is (i) (ii) and (iv) are not correct as activity F has only one immediate predecessor (iii) is not correct as E's immediate predecessor's are B and C and not C and D. Activity Optimistic Most Probable Pessimistic Expected Time Variance A 8 10 15 10.50 1.36 B 7 8 9 8.00 0.11 C 5 6 10 6.50 0.69 D 3 3 3 3.00 0.00 E 1 5 9 5.00 1.78 F 4 7 10 7.00 1.00 G 3 8 10 7.50 1.36 47.50 6.31 Paths Duration Days A-C-E-G 10.5+6.5+5+7.5 29.50 Critical path B-D-F 8+3+7 18.00 B-E-G 8+5+7.5 20.50 *Expected = (Optimistic + 4 * Probable + Pessimistic) / 6 Variance = (Pessimistic - Optimistic / 6)^2 Standard Deviation = Variance Critical path = A-C-E-G Expected Time = 29.50 days Variance = 5.19 days Standard Deviation = 2.28 days Probability that project will be completed in 30 days x 30 Z = X - Mean /Sd = 30 - 29.5 / 2.28 Z = 0.219 From Z tables, we get, Required Probability = 0.5871 or 58.71% b. Probability of completing project in 30 weeks x 30 Z = X - Mean /Sd = 30 - 26/2.0276 Z = 1.973 From Z tables, we get, Required Probability = 0.9756 OR 97.56% Activity Expected Time ES EF LS LF Slack A 10.5 0 10.5 0 10.5 0 B 8 0 8 9 17 9 C 6.5 10.5 17 10.5 17 0 D 3 8 11 19.5 22.5 11.5 E 5 17 22 17 22 0 F 7 11 18 22.5 29.5 11.5 G 7.5 22 29.5 22 29.5 0 ES = E of Tail Event EF = ES + Activity Duration LF = L of Head Event LS = LF - Activity Duration Slack - LS - ES E = Earliest occurrence time for the event L = Latest allowable time for the occurrence of event No delaying B by 6 days won't impact the overall project duration as it has a slack of 9 days. So B can be delayed by 9 days without impacting project duration

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.