$\backslash$table$[[$Activity$,\backslash$table$[[$Normal$],[$Time$],[($days$)]],\backslash$table$[[$Normal$],[$Cost $($$$)]],\backslash$table$[[$Crash$],[$Time$],[($days$)]],\backslash$table$[[$Crash$],[$Cost $($$$)]],\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[$START$,0,0,0,0,-],[$A$,10,50,8,150,$START$],[$B$,4,40,2,200,$START$],[$C$,7,70,6,160,$B$],[$D$,2,20,1,50,$A$,$ C$],[$E$,3,30,3,30,$A$,$ C$],[$F$,8,80,5,290,$B$],[$G$,5,50,4,180,$D$],[$H$,6,60,3,180,$E$,$ F$],[$FINISH$,0,0,0,0,$G$,$ H$]]$ Analyzing Cost$-$Time Trade$-$offs in Managing Projects in Supply Chains

You are in charge of a project at the local community center. The center needs to remodel one

of the rooms in time for the start of a new program. Delays in the project mean that the center

must rent other space at a nearby church at additional cost. Time and cost data for your project

are contained in table below. Your interest is in minimizing the cost of the project to the

community center.

a$)$ Using the normal times for each activity, what is the earliest date you can complete

the project?

b$)$ Suppose the variable overhead costs are $$50$ per day for your project. Also, suppose

that the center must pay $$40$ per day for a temporary room on day $15$ or beyond. Find

the minimum$-$cost project schedule.