For the project below the daily indirect cost is $$1,200.$

a$)$ Develop a PERT diagram and find the duration of the project and the critical path,

b$)$ Plot the S$-$curve for the direct $+$ indirect cost of the project assuming all activities start times to be as early as possible $($MSproject setting$).$

c$)$ What is the likelihood of finishing the project in $30$ workdays?

d$)$ Determine the $95\%$ likely duration of the project and the new total cost assuming duration change is only due to crew startup delays rather than delays in the task themselves.

e$)$ What is the probability of the slack for clearing and grubbing being less than zero?

f$)$ Does the project have any path other than the identified critical path that you need to pay attention to$?$ If so why? $($use path criticality, and also the plot of path durations with standard deviation error bar to help you discuss$).$

g$)$ Using Matlab, generate $1,000,000$ random beta distributed variables for each task duration, and carry out the Monte Carlo simulation for the network diagram, and plot the distribution of the most likely critical path, plot and determine path criticality and task criticality, comment on what you may anticipate?

$\backslash$table$[[$No$.,$Activity,Duration $($days$),$Predecessors,Cost$/$day $($$$)],[,,a,m,b,,],[1,$Start,$0,0,0,-,-],[2,$Mobilize,$1,2,3,-,2,500],[3,$Stock Materials,$2\mathrm{.}5,3\mathrm{.}75,6\mathrm{.}5,2,5,500],[4,$Clearing and Grubbing,$4,5\mathrm{.}5,10,2,1,334],[5,$Grading of Road,$6,6\mathrm{.}5,10,2,360],[6,$Finish Grade,$3\mathrm{.}5,4\mathrm{.}75,7\mathrm{.}5,3,4,600],[7,$Prefab Bleachers,$12,15\mathrm{.}75,21,3,1,125],[8,$Landscape,$11,12,13,3,4,2,915],[9,$Pave Road,$5,8\mathrm{.}25,10,5,3,750],[10,$Place Tennis Court,$9,9\mathrm{.}5,13,6,2,000],[11,$Erect $/$ paint bleachers,$5\mathrm{.}5,6\mathrm{.}5,10\mathrm{.}5,4,7,2,275],[12,$Curbing,$4,4\mathrm{.}75,7,8,9,1,200],[13,$Final Inspection$/$Clean$-$up$,2\mathrm{.}5,2\mathrm{.}75,4\mathrm{.}5,10,11,12,1,350],[16,$Finish,$0,0,0,,-]]$