$4.$ A project has the following activities:

Normal Normal Crash Crash

Immediate Time Cost Time Cost

Activity Predecessors $($weeks$)($$$)($weeks$)($$$)$

A none $43,00035,000$

B A $95,00078,000$

C A $47,00047,000$

D B$,$ C $66,00048,000$

E C $84,00068,000$

F D $34,00029,000$

G E$,$ F $42,00027,000$

a$)$ Draw the network diagram based on normal time.

b$)$ What are potential paths $($connected paths$)$ and corresponding durations?

c$)$ What is the expected project completion time based on normal time?

d$)$ What is the most economical way and how much will it cost to reduce the completion time of the project by three weeks?