Consider the (simplified) list of activities and predecessors that are involved in building a house (Table 20). a Draw a project network, determine the critical path, find the total float for each activity, and find the free float for each activity. b Suppose that by hiring additional workers, the dura- tion of each activity can be reduced. The costs per day of reducing the duration of the activities are given in Table 21. Write down the LP to be solved to minimize the total cost of completing the project within 20 days. TABLE 20 Activity Description Immediate Predecessors Duration (Days) A Build foundation 5 B Build walls and ceilings A 8 C Build roof B 10 D Do electrical wiring B 5 E Put in windows B 4 F Put on siding E 6 G Paint house C. F 3 TABLE 21 Activity Cost per Day of Reducing Duration of Activity ($) Maximum Possible Reduction in Duration of Activity (Days) Foundation 30 2 Walls and ceiling 15 3 Roof 20 1 Electrical wiring 40 2 Windows 20 2 Siding 30 3 Paint 40 1

Consider the (simplified) list of activities and predecessors that are involved in building a house (Table 20). a Draw a project network, determine the critical path, TABLE 20 find the total float for each activity, and find the free Immediate Duration Activity Description Predecessors (Days) float for each activity. A Build foundation b Suppose that by hiring additional workers, the dura- B Build walls and ceilings A C B 10 tion of each activity can be reduced. The costs per day Build roof D Do electrical wiring B 5 of reducing the duration of the activities are given in Put in windows B Table 21. Write down the LP to be solved to minimize Put on siding E wat the total cost of completing the project within 20 days. Paint house C, F TABLE 21 Maximum Possible Cost per Day of Reduction in Reducing Duration Duration of Activity of Activity ($) Activity (Days) Foundation 30 Walls and ceiling 15 Roof 20 Electrical wiring 40 - W N N - W N Windows 20 Siding 30 Paint 40