Given the following project: Activity Predecessor Normal Time (day) Normal Cost  ($) Crash Time (day) Crash Cost  ($) A - 4 800 2 1300 B - 10 1200 7 2400 C A 6 1100 4 1700 D A,B 7 1000 4 1600 E C 10 2000 8 3000 F C,D 5 900 - - (a) Draw the network and find the critical path duration of the project, total cost of project using normal times.   (b) Calculate the maximum time reduction and crash cost-per-day (all activities may be partially crashed) for each activity. Then fill the table below. (Note: Activity “F” cannot be crashed) Activity Maximum Time Reduction (day) Cost to Crash per Period ($/day) A     B     C     D     E     F     (c) Find the optimal way of getting a 20-day delivery time. What is the project cost? (d) Find the optimal way of getting a 18-day delivery time. What is the project cost?

2. The time estimates (in weeks) for the activities of a PERT network are given below. (i) (ii) 1-2 1-3 1-4 2-5 3-5 4-6 5-6 18 9 10 8 16 7 Activity to 24 16 3 tm 7 9 20 14 2 tp 9 20 11 11 28 18 4 Draw the project network and calculate the project length. Calculate the standard deviation and variance along the critical path. (iii) Find the probability of completing the project one day earlier and 2 days later.

4 01:34:47 The network diagram and task times for a project are shown below. A₁ A2 Late start time A3 Task A₁ A₂ A3 A₁ A5 What is the late start time for activity A3 ? Duration (days) 7 6644 A4 days A5

PERT-CPM Yu and Mi Company is planning to computerize its accounting system. Its IT consultant has determined the following activities required to complete this project together with the time estimates and precedence relationships. Time estimates (weeks) Optimistic Most Likely Pessimistic 5 Activity Description Predecessor Recruit project personnel System development System training Equipment training Manual system test Prel. System changeover Computer-personnel interface Equipment redesign Equipment testing J A 8 12 17 B 3 15 C A 4 7 10 D A 8 23 В. С В. С D, E D, E E F 1 1 1 1 4 13 3 H 1 2.5 7 I H 1 1 1 System debugging and installation Equipment changeover F, G G, I K 5 8. 11 a. Determine the expected project completion time and the variance. b. What is the project's critical path? c. Determine the probability that the project will be completed in 40 weeks or less.