A simple project listing of five activities, their predecessors, and their respective time estimates are presented here: Using CPM, what is the latest finish time for the last activity in this project (i.e., the total time to complete the project)?
A) 10 days
B) 7 days
C) 8 days
D) 12 days
E) 9 days

Question

A simple project listing of five activities, their predecessors, and their respective time estimates are presented here:  Using CPM, what is the latest finish time for the last activity in this project (i.e., the total time to complete the project)?
A) 10 days 
B) 7 days 
C) 8 days 
D) 12 days 
E) 9 days

Quizplus · Accepted Answer

Using CPM, we can calculate the earliest start time (EST), earliest finish time (EFT), latest start time (LST), and latest finish time (LFT) for each activity. We start by identifying the predecessor(s) for each activity:
Activity A has no predecessors, so EST and EFT are both 0. 
Activity B has A as its predecessor, so EST is 4 (the EFT of A) and EFT is 6 (EST + time estimate of B). 
Activity C has A as its predecessor, so EST is 0 (the EFT of A) and EFT is 5 (EST + time estimate of C). 
Activity D has B and C as its predecessors, so EST is 6 (the larger EFT of its predecessors) and EFT is 10 (EST + time estimate of D). 
Activity E has D as its predecessor, so EST is 10 (the EFT of D) and EFT is 12 (EST + time estimate of E). 
Next, we can calculate the LST and LFT for each activity starting from the end:
Activity E has no successors, so LFT and LST are both 12. 
Activity D has E as its successor, so LFT is 12 (the LST of E minus the time estimate of D) and LST is 8 (LFT minus time estimate of D). 
Activity B has D as its successor, so LFT is 8 (the LST of D minus the time estimate of B) and LST is 4 (LFT minus time estimate of B). 
Activity C has no successors, so LFT and LST are both 7. 
Activity A has B and C as its successors, so LFT for A is 4 (the smaller LST of its successors minus its own time estimate of 2) and LST is 0 (the larger EST of its successors). 
Therefore, the latest finish time for the last activity (E) is 12, so the total time to complete the project is 12 days. Therefore, the answer is D.

A Simple Project Listing of Five Activities, Their Predecessors, and Their