Table $1.$ Activity times in weeks

$\backslash$table$[[$Activity$,$Description,$\backslash$table$[[$Optimistic$],[$Time$]],\backslash$table$[[$Most Likely$],[$time$]],\backslash$table$[[$Pessimistic$],[$time$]],\backslash$table$[[$Immediate$],[$Predecessor$]]],[$A$,$Site Preparation,$3,4,11,-],[$B$,$Foundation Construction,$8,9,10,$A$],[$C$,,10,13,16,$B$],[$D$,$Roofing Installation,$3,4,5,$C$],[$E$,$Exterior Wall Construction,$8,9,10,$C$],[$F$,$Window and Door Installation,$4,5,6,$E$],[$G$,\backslash$table$[[\backslash$table$[[$Plumbing and Electrical$],[$Rough$-$In$]]]],10,10,16,$D$,$E$],[$H$,$HVAC System Installation,$3,4,5,$G$],[$I$,$Insulation Installation,$4,5,6,$G$],[$J$,$Drywall Installation,$4,4,4,$G$],[$K$,$Interior Finishing,$12,13,14,$F$,$H$,$I,J$],[$L$,$Flooring Installation,$4,5,6,$K$],[$M$,\backslash$table$[[$Cabinetry and Built$-$In$],[$Furniture Installation$]],4,4,10,$K$],[$N$,$Painting and Wallpapering,$3,4,5,\backslash$bar $($K$)],[$O$,\backslash$table$[[$Fixture and Appliance$],[$Installation$]],4,5,6,$K$],[$P$,\backslash$table$[[$Landscaping and Outdoor$],[$Features$]],8,10,12,$E$],[$Q$,$Swimming Pool Construction,$10,10,16,$P$],[$R$,$Security System Installation,$3,4,8,$K$,$Q$],[\backslash$bar $($S$),\backslash$table$[[$Final Inspection and Quality$],[$Control$]],2,3,4,$L$,$M$,$N$,$O$,$R$],[$T$,$Handover and Occupancy,$1,1,1,$S$]]$ Questions Part A:

QB has a policy of passing all the construction plans through a project review committee of

colleagues. This committee traditionally checks that all details are covered, times are realistic, and

resources are available. To be ready to answer project committee queries, Fatima wishes you to do

the followings:

a$.$ Develop a report that presents a planned schedule and expected project completion time in

weeks. Include a Gantt chart and project network in your report using MS Project.

b$.$ Find the probability of completing this project in $78$ weeks $($one and half year$).$

c$.$ In addition, find out what expected completion time will ensure nearly $95\%$ chance of

completing the project in $78$ weeks.

d$.$ Find the probability of finishing this project in $70$ weeks.

e$.$ Find the probability of finishing this project in $65$ weeks. please answer the question Al$-$Qasr Builders, Inc. $($QB$)$ is a specialized firm that constructs private home dwellings for rich

customers. QB uses a standardized project format for each assignment of house construction

projects. Only activity times and unusual circumstances change the standard network. Fatima $Al$

Khurasaani has been assigned to a rich client as project manager to construct a beautiful mansion

for him. The rich client is known as Abu Hatem for his generosity and kindness. Fatima has told

Abu Hatem that a mansion of this size would typically be completed in one year and six months

$($about $78$ weeks$).$ Abu Hatem wants Fatima to complete the project three months earlier, before

his son's marriage, which is scheduled to take place in about $15$ months from now in one year and

three months $($about $65$ weeks$).$ He has told Fatima that if the mansion is completed in $65$ weeks,

he will give the firm $$100,000$ extra as a bonus besides paying the negotiated construction price

of $$3$ million for the mansion. He has also further added that for any further reduction from $65$

weeks, he would compensate the firm with $$10,000$ per week. Fatima has compiled the network

information and activity times for this project, given in Table $1,$ as follows: