$\backslash$table$[[$A: Concept development,Optimistic time $($months$),,24],[$Plan definition,$3,,],[$B$.$ Define project scope,,$2,12],[$C$.$ Develop broad schedule,$1,\backslash$table$[[2],[0\mathrm{.}5]],1],[$D$.$ Detalled cost estimates,$0\mathrm{.}25,\backslash$table$[[0\mathrm{.}5],[0\mathrm{.}3]],0\mathrm{.}5],[$E$.$ Develop staffing plan,$0\mathrm{.}2,\backslash$table$[[0\mathrm{.}3],[0\mathrm{.}3]],0\mathrm{.}6],[$Design and construction,$0\mathrm{.}2,,],[$F$.$ Detailed engineering,,,$6],[$G$.$ Facility construction,$\backslash$table$[[2],[8]],3,24],[$H$.$ Mobilization of employees,$\backslash$table$[[8],[0\mathrm{.}5]],12,4],[$I$.$ Procurement of equipment,$\backslash$table$[[0\mathrm{.}5],[1]],2,12],[$Startup and Turnover,$1,3,],[$J$.$ Pre$-$startup inspection,,,$1],[$K$.$ Recruiting and training,$\backslash$table$[[0\mathrm{.}25],[0\mathrm{.}25]],0\mathrm{.}5,1],[$L$.$ Solving startup problems,$\backslash$table$[[0\mathrm{.}25],[0]],0\mathrm{.}5,2],[$M$.$ Centerlining,$\backslash$table$[[0],[0]],1,4]]$

Questions

Draw a network diagram for this project. Identify all paths through the network diagram.

Simulate the completion of this project $1,000$ times, assuming that activity times follow a BetaPERT distribution. Estimate the mean and standard deviation of the project completion time.

Develop a histogram to summarize the results of your simulation.

Calculate the probability that the project can be completed within $30$ months. What is the probability that the project will take longer than $40$ months? What is the probability that the project will take between $30$ and $40$ months?

What path has the longest expected time? What is the probability that this path will be the critical path?