For the network shown: $($Problem $17,$ Chapter $5$ Projects $$ OPERATIONS AND SUPPLY CHAIN MANAGEMENT THE CORE $4$TH EDITION $$ JACOBS & CHASE$)$

a$.$ Determine the critical path and the early completion time in weeks for the project.

b$.$ For the data shown, reduce the project completion time by three weeks. Assume a linear cost per week shortened, and show, step by step, how you arrived at your schedule.