Problem 3. (23 marks in total) The 21st Century Studios is about to begin the production of its most important and most expensive) movie of the year. The movie's producer, Dusty Hoffmer, has decided to use PERT/CPM to help plan and control this key project. He has identified the eight major activities (labeled A, B,..., H) required to produce the movie. The activities, precedence relationships, estimated completion times, and cost details are shown in the below table. Time (in weeks) Cost (in $ millions) Precedence Activity Relationship Normal Crash Normal Crash B D E F G H B B E D S 3 4 6 5 7 9 8 4 5 24 13 21 30 26 35 30 35 36 25 29 50 36 57 53 51 (a) (7 marks) Draw the project network, Please report the earliest start, the earliest finish, the latest start and the latest finish of each activity on your diagram. (b) (1 mark) Under normal circumstances, what is the completion time of the project? (c) (3 marks) What are the slack of each activity? (d) (2 marks) Under normal circumstances, what is the total cost of the project? (c) (10 marks) Formulate an LP model to determine an optimal crashing for each of the activities in order to complete the project within 15 weeks