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. 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 PartialPayment

$4$ $$1,000$

$5$ $$3,500$