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$]]$ 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: