Pirmin's Bike Shop is behind on a custom bike and needs to crash $8$ hours of time from the $8-$step project. Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash.

Activity Normal Duration $($hours$)$ Normal Cost $($$$)$ Crash Duration $($hours$)$ Crash Cost $($$$)$ Immediate Predecessors

A $210117-$

B $315223$ A

C $525430$ B

D $320124$ C

E $630445$ C

F $240160$ E

G $735650$ F

H $1050780$ D$,$G

a$.$ What is the critical path?

b$.$ What is the project length?

c$.$ Which activity should the bike shop crash first $,$ and how much would it add to the project cost?

d$.$ Which activity should be crashed next to reduce an additional hour off the project $,$ and what would be the total cost? $($reducing the project by $2$ hours$)$

e$.$ Which activity$($s$)$ should be crashed next if you needed to reduce the project by another $2$ hours $($total $4$ hours$)$ and what would be the total cost for the $4$ hour reduction