Payment scheduling and PERT Problem $2(35$ pts$)$ Consider the project information below. Assume that the overhead cost of the project is $$75$ per unit time. Activity Normalduration Normalcost$($$$)$ Crashduration CrashCost$($$$)$ A $(1,2)9$ $$1506$ $$300$ B $(1,3)5$ $$1103$ $$250$ C $(1,4)4$ $$902$ $$160$ D $(2,6)7$ $$1455$ $$208$ E $(3,5)7$ $$1454$ $$306$ F $(4,5)4$ $$983$ $$125$ G $(5,6)6$ $$764$ $$198$ a$)$ What is the optimal project duration that will minimize the sum of direct and indirect costs and what is the total cost of this project? $(15$ points$)$ b$)$ The following payment schedule is associated with some events $($nodes$).$ The interest rate is $15\%($r $=0\mathrm{.}15).$ Find the optimal payment schedule for this project. $(20$ points$)$ Event Partial Payment $4$ $$1,0005$ $$3,500$