$(8$ points$)$ Lindsey Brinton is moving into a rental house near campus at the beginning of the new fall semester at Tech with three friends. Each of the four friends will have a bedroom that they can redecorate as they wish. Lindsey wants to wallpaper her room and put down a new carpet, and she has identified the following activities and the times they will take that she will need to accomplish to complete the project before school starts.

$\backslash$table$[[$Activity$,$Description,$\backslash$table$[[$Activity$],[$Predecessor$]],\backslash$table$[[$Time Estimate$],[($hours$)]]],[$a$,$Clean walls,$-,6],[$b$,$Wash and clean woodwork,a$,4],[$c$,$Select and buy paint,$-,6],[$d$,$Paint woodwork $($first coat$),$b$,$ c$,5],[$e$,$Fill holes,a$,3],[$f$,$Select and buy wallpaper,b$,$ c$,4],[$g$,$Paper walls,d$,$ e$,$ f$,10],[$h$,$Paint woodwork $($second coat$),$d$,4],[$i$,$Lay new carpet,g$,$ h$,8],[,,,]]$

a$)$ Construct and show the network for this project, showing all precedence arrows, earliest start, earliest finish. latest start, latest finish, and slack times.

b$)$ What is the critical path?

c$)$ What is the project duration time? hours