$18.$Launching a New Track and Field Program. Due to population growth in the area, the new Liberty High School has just opened in a local school district. The athletic director at Liberty High is planning the launch of the school's track and field team. The first team practice is scheduled for April $1.$ The activities, their immediate predecessors, and the activity time estimates $($in weeks$)$ are listed in the following table. LO $1,2,3,4$ImmediateTime $($weeks$)$ActivityDescriptionPredecessorOptimisticMost ProbablePessimisticAMeet with board$112$BHire coachesA$468$CConduct fundraiserA$246$DAnnounce programB, C$123$EMeet with coachesB$234$FOrder team equipmentA$123$GRegister athletesD$123$HReserve buses for meetsG$123$IPlan first practiceE, H$,$ F$111$a$.$Draw a project network.b$.$Develop an activity schedule.c$.$What are the critical activities, and what is the expected project completion time?d$.$If the athletic director plans to start the project on January $1,$ calculate the probabil$-$ity the track and field team will be ready by the scheduled April $1$ date $(13$ weeks$)$ based solely on the critical path. Should the athletic director begin planning the track and field team before January $1?$