Kim's engineering has a plan to build a new factory to expand their business. Consider the project with the following dependency matrix and the expected time for each activity.

$\backslash$table$[[$Activity$,$Predecessor,Activity Time $($Month$)],[$A$1,,3],[$A$2,$A$1,4],[$A$3,$A$1,5],[$A$4,$A$1,6],[$A$5,$A$1,7],[$A$6,$A$2,$ A$3,$ A$4,8],[$A$7,$A$5,$ A$6,9],[$A$8,$A$7,10]]$

Draw an activity network diagram and compute the total slack time of the project $(20$ points$)$