****ONLY PART (E) PLEAE AND THANK YOU ****

Problem 3. (23 marks in total) A company is planning to launch a project to develop a new product. The company's contract with a consultant calls for project completion within 92 weeks, with penalties imposed for late delivery. The activities, precedence relationships, estimated completion times, and cost details are shown in the table below. Time Cost Activity Precedence Relationship Normal Crash Normal Crash A 32 weeks 28 weeks $180 million B 28 weeks 25 weeks $146 million A 36 weeks 31 weeks $210 million D E B 16 weeks 32 weeks 13 weeks 27 weeks $72 million $160 million $160 million $125 million $170 million $60 million $135 million $215 million $90 million $120 million $190 million $80 million F B 54 weeks 47 weeks $257 million G D E,G 17 weeks 20 weeks 15 weeks 17 weeks $96 million $132 million H 1 E,G 34 weeks 30 weeks $226 million J CAF 18 weeks 16 weeks $84 million 3 (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 critical activities? Why are those activities so? (d) (2 marks) Under normal circumstances, what is the total cost of the project? (e) (10 marks) Formulate an LP model to determine an optimal crashing for each of the activities in order to complete the project within the required 92 weeks