Consider a project with the activity precedence relationships and time estimates given in the following table.

$\backslash$table$[[$Activity$,$Predecessors,Duration$],[$A$,-,6],[$B$,$A$,12],[$C$,$A$,4],[$D$,$B$,$C$,10],[$E$,$C$,10]]$

Two workers are available. Due to his skill set, Jack is responsible for activities A and B$.$ Similarly, only Amy can do activities C$,$ D and E$.$

$($a$)$ Assuming that the time estimates are perfectly accurate, what is the expected project duration? Explain. $($Use the time estimates as is; do not insert project or feeding buffers.$)(1$ point$)$

$($b$)$ Use the ideas from the Critical Chain to reformulate the project schedule using project and feeding buffers. Include a diagram similar to that discussed in class. $(3$ points$)$

$($c$)$ Assume Jack and Amy can be cross trained to do any activity, but will not share activities. Can the activities be reassigned to Jack and Amy such that the project is completed in less time? If so$,$ indicate the new assignment and project duration. $(2$ points$)$

$($d$)$ Consider the following assignment: Jack does activities A and D$,$ Amy does activities B$,$ C and E$.$ Use the ideas from the Critical Chain to reformulate the project schedule using project and feeding buffers. Include a diagram similar to that discussed in class. $(4$ points$).$