Bakersfield Pools is about to work on a project to install a backyard pool and build an accompanying bathhouse. The installation process is fairly well defined. Building the pool involves digging the foundation, pouring concrete, and ordering and installing a filtration system. The bathhouse work involves constructing the bathhouse, installing the additional required plumbing, and installing the necessary electrical work. The process is shown in the table below.

$\backslash$table$[[$Activity$,$Description,$\backslash$table$[[$Immediate$],[$Predecessors$]],$Duration$],[$A$,$Dig pool foundation,$-,10],[$B$,$Order filtration system,$-,1],[$C$,$Receive filtration system,B$,9],[$D$,$Pour concrete,A$,3],[$E$,$Install filtration system,C$,$ D$,13],[$F$,$Construct bathhouse,$-,23],[$G$,$Install electrical wiring,F$,2],[$H$,$Install plumbing,F$,3],[$I$,$Connect water supply,H$,2],[$J$,$Test,E$,$ G$,$ I,$2]]$

Answer the following questions. Ignore the possibility of crashing until part f$).$

a$)$ Draw the network diagram for the project. Calculate early start, early finish, late start, late finish, and slack times.

b$)$ Bakersfield Pools works all $7$ days a week. The customer wants this pool completed in time for a birthday party in $27$ days. Can it be done? Why or why not? $($Note: this means the entire project must be completed.$)$ Crashing is NOT possible at this point.

c$)$ The staff member who is in charge of pouring concrete wants to go on a two$-$week vacation starting in $12$ days. Can Bakersfield Pools let him go when he wants? Why or why not?

d$)$ Equipment required to do task $E($the installation of the filtration system$)$ is currently undergoing repairs. Until it is repaired, no work can be done on task $E.$ What is the latest day those repairs can be completed by without delaying the project? Give your reasoning. A$-$D please