Consider the project described in problem $1$ with the normal and the expedited costs and times given in the following table.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$]],\backslash$table$[[$Normal$],[$Time$]],\backslash$table$[[$Expedited$],[$Time$]],\backslash$table$[[$Normal$],[$Cost$]],\backslash$table$[[$Expedited$],[$Cost$]]],[$A$,-,3,2,$$$200,$$$250],[$B$,$A$,5,3,600,850],[$C$,$A$,1,1,100,100],[$D$,$B$,$ C$,4,2,650,900],[$E$,$B$,3,2,450,500],[$F$,$E$,$ D$,3,2,500,620],[$G$,$F$,2,1,500,600],[$H$,$E$,$ D$,4,2,600,900]]$

a$.$ Consider successive reductions in the project time of one week and find the direct cost of the project after each reduction.

b$.$ Suppose that indirect costs are $$150$ per week. Find the optimal project completion time and the optimal total project cost.