For following problems, formulate Linear Programs clearly describing variables, objective function, and constraints. Solve the problems using Excel Solver. 1. Mary is planning her wedding and develops the following preliminary information. Activity A (select wedding date) Immediate Predecessor none Estimated Normal Time 1 week B (select wedding location) none 4 weeks C (guest list, whose attending) D (select entertainment) A, B 3 weeks A 4 weeks E (choose catering) A, C 3 weeks F (wedding day) D, E 0 weeks a. b. c. d. e. Draw the network for this project. What is the critical path(s)? What is the project completion time? What activity has the most slack? What wedding activities did Mary leave out of her analysis? List them and now redraw the project network (but do NOT try to assign activity times or work out the new solution). What did you learn? 2. A competitor of Kozar International, Inc. has begun marketing a new instant developing film project. Kozar has had a similar product under study in its R&D department but has not yet been able to begin production. Because of the competitor's action, top managers have asked for a speedup of R&D activities so that Kozar can produce and market instant film at the earliest possible date. The predecessor information and activity time estimates in months are shown in the next column. Activity A B C D E F G Immediate Predecessor A A B, C B C, D, E E Optimistic Time 1 3 1 3.5 4 6.5 5 Most Probable Time 1.5 4 2 5 5 7.5 9 Pessimistic Time 5 5 3 6.5 12 11.5 13 a. Draw the project network. b. Develop an activity schedule for this project using early and late start and finish times, compute activity slack time, and define the critical activities. c. What is the probability of finishing the project in 32 months? 3. A computer-system installation project consists of eight activities. The immediate predecessors and activity times in weeks are shown below. Activity A B C D E F G H Immediate Predecessor A B, C D E B, C F, G Activity Time 3 6 2 5 4 3 9 3 a. Construct an early-start-date Gantt chart for the computer-system installation project. b. As a project manager, where would you focus your attention, given your analysis? 4. Environment Recycling, Inc. must clean up a large automobile tire dump under a state environmental cleanup contract. Some of the activities can be crashed. The tasks, durations (in weeks), costs, predecessor relationships, the crash times, and costs associated with performing the activities at their original (normal) times and for the crash times are shown as follows: Activity A B C D E F G H I Immediate Predecessor A A B, D, C D D E F, G, H Normal Time Crash Time 5 8 7 6 8 3 3 4 6 4 6 6 5 6 2 2 3 5 a. Find the total project completion time Normal Cost ($) 400 1,800 800 600 1,700 800 500 400 900 Crash Cost ($) 750 2,200 1,100 1,000 2,200 1,000 650 600 1,300 b. Find the lowest cost solution if the state wants to complete the project three weeks early