Problem $3$

For the project in Problem $2,$ assume the task times are variable, with the optimistic, most likely, and pessimistic task times as follows:

$\backslash$begin$\{$tabular$\}\{|$c$|$l$|$c$|$c$|$c$|\}$

$\backslash$hline & & & TASK TIME $($DAYS$)$ & $\backslash \backslash$

$\backslash$hline TASK & DESCRIPTION & OPTIMISTIC & MOST LIKRLY & PESSIMISTIC $\backslash \backslash$

$\backslash$hline A & Inspect the house & $2$ & $4$ & $5\backslash \backslash$

$\backslash$hline B & Appraise the house & $1$ & $3$ & $5\backslash \backslash$

$\backslash$hline C & Do the title search & $3$ & $4$ & $6\backslash \backslash$

$\backslash$hline D & Get the tax clearance & $3$ & $5$ & $10\backslash \backslash$

$\backslash$hline E & Get the sales permit & $1$ & $2$ & $2\backslash \backslash$

$\backslash$hline F & Find a buyer & $7$ & $21$ & $42\backslash \backslash$

$\backslash$hline G & Get a mortgage & $7$ & $14$ & $30\backslash \backslash$

$\backslash$hline H & Get the legal documents & $5$ & $10$ & $14\backslash \backslash$

$\backslash$hline I & File the legal documents & $1$ & $1$ & $1\backslash \backslash$

$\backslash$hline J & Final closing & $1$ & $1$ & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$.$ Compute by hand the earliest expected completion time of the project, identify the critical tasks and path$($s$),$ and determine the variance of the project's completion time. $(10$ points$)$

b$.$ Use Excel QM to venify your computations in part $($a$).(5$ points$)$