Problem 1: Cray Computer Corporation is developing a new super computer. The table below lists the project activities, normal and crash times, and normal and crash costs. Immediate Time (weeks) Cost ($1,000s) Activity Description Predecessor(s) Normal Crash Normal Crash Design 90 90 Build prototype A 125 170 Evaluate equipment A 80 100 Write methods report A 50 80 Test prototype B, C 140 160 Write equipment report D 20 30 Write final report E F 45 105 a). Draw an activity network diagram for this project. Using the normal activity times, determine the early start, early finish, late start, and late finish times for each activity. Record these values in the diagram. b). Based on the normal activity times and costs: (i) How long will it take to complete the project? (ii) What is the total project cost? (ii) Identify the critical path(s)