Allen Machines specializes in developing weed-harvesting equipment that is used to clear small lakes of weeds. Allen Machines is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities and time in weeks necessary to build one of these experimental machines are shown in the table below.

Activity Immediate Predecessors Time in Weeks
A none 6
B none 5
C A 3
D A 2
E B 4
F B 6
G C,E 10
H D,F 7

1. What is the minimum possible time required for completing the project?
2. What is the latest possible time that Activity D may be started without delaying the completion of the project?
3. What is the latest finish time for Activity F?
4. What is/are the critical path(s)?


2. The following is the activity and associated costs for the renovation of the local high school football stadium. The times are in weeks.

Activity Immediate Predecessor Time Cost ($)
A - 4 25,000
B - 5 30,000
C A 3 15,000
D B 8 50,000
E B 2 12,000
F C, D 3 15,000
G C, D 7 46,000
H E, F 2 20,000

1. What is the critical path for this project?
2. How much of the total budget would be spent in Week 8 (Period 8) with the earliest start budget?