MS $3053-$ Problem Set #$10$

Due Date: December $3,2024$

#$1$

The manager of a local sports club is planning its soccer season. The activities, their immediate predecessors, and the activity time estimates $($in weeks$)$ are as follows.

$\backslash$table$[[,,$Time $($weeks$),],[$Activity$,$Description,Predecessor$($s$),$Optim.,Most Likely,Pessim.$],[$A$,$Meet with board,$-,1\mathrm{.}00,1\mathrm{.}50,2\mathrm{.}25],[$B$,$Interview$/$hire coaches,A$,3\mathrm{.}00,4\mathrm{.}25,5\mathrm{.}50],[$C$,$Reserve fields,A$,2\mathrm{.}50,3\mathrm{.}25,4\mathrm{.}00],[$D$,$Create schedule,B$,$ C$,1\mathrm{.}50,2\mathrm{.}00,2\mathrm{.}50],[$E$,$Meet with coaches,B$,2\mathrm{.}50,3\mathrm{.}25,4\mathrm{.}50],[$F$,$Register players,A$,1\mathrm{.}00,2\mathrm{.}00,4\mathrm{.}00],[$G$,$Order uniforms,D$,1\mathrm{.}00,2\mathrm{.}00,3\mathrm{.}00],[$H$,$Collect fees,G$,1\mathrm{.}00,2\mathrm{.}00,6\mathrm{.}00],[$I$,$Organize first practice,E$,$ F$,$ H$,0\mathrm{.}50,1\mathrm{.}00,2\mathrm{.}00]]$

$($a$)$ Draw the project network diagram.

$($b$)$ Compute the mean and variance of the duration of each activity. $($You may do this by hand or by using technology, such as Excel.$)$

$($c$)$ Determine the critical path, the expected project duration, and the variance of the project duration.

$($d$)$ What is the probability that the planning process is completed within $13\mathrm{.}9$ weeks?

$($e$)$ What is the probability that the planning process takes longer than $12\mathrm{.}4$ weeks?

$($f$)$ If the manager wants a $92\mathrm{.}5\%$ probability of completing the planning process on time, how far ahead of the first practice should they start the project?