I.$$ The following table $($attached$)$ represents a plan for a project:

$$a$.$ Construct the appropriate network diagram.

b$.$ Indicate the critical path.

c$.$ What is the expected completion time for the project?

d$.$ You can accomplish any one of the following at an additional cost of

$$1,500$:

i$.$ Reduce job $5$ by two days.

ii$.$ Reduce job $3$ by two days.

iii.$$ Reduce job $7$ by two days.

If you will save $$1,000$ for each day that the earliest completion time is reduced, which action, if any, would you choose?

e$.$ What is the probability that the project will take more than $30$ days to complete? $\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Times in days$\}$ & & $\backslash \backslash$

$\backslash$hline Activity & Predecessors & a & m & b & ET & Var $\backslash \backslash$

$\backslash$hline $1$ & $-$ & $2$ & $3$ & $4$ & $3$ & $0\mathrm{.}11\backslash \backslash$

$\backslash$hline $2$ & $1$ & $1$ & $2$ & $3$ & $2$ & $0\mathrm{.}11\backslash \backslash$

$\backslash$hline $3$ & $1$ & $4$ & $5$ & $12$ & $6$ & $1\mathrm{.}78\backslash \backslash$

$\backslash$hline $4$ & $1$ & $3$ & $4$ & $11$ & $5$ & $1\mathrm{.}78\backslash \backslash$

$\backslash$hline $5$ & $2$ & $1$ & $3$ & $5$ & $3$ & $0\mathrm{.}44\backslash \backslash$

$\backslash$hline $6$ & $3$ & $1$ & $2$ & $3$ & $2$ & $0\mathrm{.}11\backslash \backslash$

$\backslash$hline $7$ & $4$ & $1$ & $8$ & $9$ & $7$ & $1\mathrm{.}78\backslash \backslash$

$\backslash$hline $8$ & $5,6$ & $2$ & $4$ & $6$ & $4$ & $0\mathrm{.}44\backslash \backslash$

$\backslash$hline $9$ & $8$ & $2$ & $4$ & $12$ & $5$ & $2\mathrm{.}78\backslash \backslash$

$\backslash$hline $10$ & $7$ & $3$ & $4$ & $5$ & $4$ & $0\mathrm{.}11\backslash \backslash$

$\backslash$hline $11$ & $9.10$ & $5$ & $7$ & $8$ & $6\mathrm{.}83$ & $0\mathrm{.}25\backslash \backslash$

$\backslash$hline

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