5. (20 points total) A company specializing in custom-engineered equipment is planning to submit a proposal to the National Aeronautics and Space Administration (NASA) to build an assembled component for a new space station that NASA plans to launch into orbit. The winning proposal will be selected on the basis of both cost and timely delivery. Also, there will be a penalty clause in the NASA contract for late delivery. The company has developed the schedule of activities that are required to produce the assembled component. The activities and precedence requirements are presented in the table below. Three time estimates (in weeks) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? Activity b df h j Immediate predecessor c, d d eff,gh, i Optimistic time (weeks) 2 15 7 20 17 Most likely time (weeks) 5 24 16 26 23 7 12 Pessimistic time (weeks) 39 20 PERT network diagram. a b 8 10 5 4 10 10 14 9 8 24 19 24 32 35 13 10 15,2439 10.14.24 b 5.9.13 h 5.8.11 8,16,24 20.26.32 10.12.20 a f j 7,10,13 i 7.10.19 17,2335 d (a) PERT network analysis: Activity T. 2 Critical ES EF LS LF S a 5 0 5 b 7.11 d 11 15 5.44 f 26 24 h 1.78 i 7 2.78 What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? Tcomp weeks