) Find earliest start time, latest start time, earliest finish time, latest finish time and slack time of all activities. Show the critical path

1. Project Planning (40 pts). Consider the list of activities and predecessors that are involved in building a house. Immediate Predecessors Duration (days) Activity A B D E F Description Build foundation Build walls and ceilings Build roof Do electrical wiring Put in windows Put on siding Paint house A,B A, B A,B C,E D, F 8 10 5 4 6 3 a) (10 pts) Draw the network. b) (15 pts) Find earliest start time, latest start time, earliest finish time, latest finish time and slack time of all activities. Show the critical path. c) (15 pts) Suppose that by hiring additional workers, the duration of each activity can be reduced. The costs per day of reducing the duration and maximum possible reduction in duration of the activities are given below. Write down the LP to be solved to minimize the total cost of completing the project within 20 days. Activity A B C D E F Description Build foundation Build walls and ceilings Build roof Do electrical wiring Put in windows Put on siding Paint house Cost per day of reducing duration of activity ($) 30 15 20 40 20 30 40 Maximum possible reduction in duration of activity (days) 2 3 1 2 2 3 1