1. Consider the network described in the table below. Immediate Predecessor(s) Pessimistic 15 Activity J K L M N Optimistic 8 7 5 9 10 Probable 10 8 6 3 5 7 8 3 J J KM KM LN 3 9 1 O 10 10 4 3 P a. Calculate the expected duration of each activity. b. Calculate the expected duration and variance of the critical path. c. Calculate the probability that the project will be completed in fewer than 30 time units. 2. The network below represents a project being analyzed by Critical Path Methods. Activity durations are indicated on the network. A 6 11 K 5 E End Start B 7 3 F H . 3 a. Identify the activities on the critical path. b. What is the duration of the critical path? c. Calculate the amount of slack time at activity H. d. If activity I were delayed by ten time units, what would be the impact on the project duration? 3. Pirmin's Bike Shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project. Given the project table below calculate the crash cost for 8 hours of time-savings. Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash. Calculate both the maximum time-savings available on a $25 crash budget and the cost to crash four hours of savings. Immediate Predecessors None Activity A B D Normal Duration (hours) 2 3 5 3 6 1 Crash Duration (hours) 2 2 4 Normal Cost ($) 10 15 25 20 30 5 35 50 Crash Cost (S) 0 23 30 24 45 0 50 A B 1 C E 4 F G 1 6 C F D G 7 H 10 7 80