Please answer PART B$.$ Thank you!

Problem $6.$ Suppose we are given a directed acyclic graph $($DAG$)\backslash ($ G$=($V$,$ E$)\backslash )$ whose nodes represent jobs, and whose edges represent precedence constraints. Specifically, each edge $\backslash ($ u $\backslash$rightarrow v $\backslash )$ indicates that job $\backslash ($ u $\backslash )$ must be completed before job $\backslash ($ v $\backslash )$ can begin. Each node $\backslash ($ v $\backslash )$ also has a weight $\backslash ($ T$($v$)\backslash )$ indicating the time required to execute job $\backslash ($ v $\backslash ).$

$($a$)$ Describe an algorithm to determine the shortest interval of time in which all jobs in $\backslash ($ G $\backslash )$ can be completed.

$($b$)$ Suppose the first job starts at time $0.$ Describe an algorithm to determine, for each vertex $\backslash ($ v $\backslash ),$ the earliest time at which job $\backslash ($ v $\backslash )$ can begin.

$($c$)$ Now describe an algorithm to determine, for each vertex $\backslash ($ v $\backslash ),$ the latest time at which job $\backslash ($ v $\backslash )$ can begin without violating the precedence constraints or increasing the overall completion time $($computed in part $($a$)),$ assuming that every job except $\backslash ($ v $\backslash )$ starts at its earliest start time $($computed in part $($b$)).$