Assignment: Cost Estimation and Analysis Exercises for Project Management Exercise $1$: Project Network Analysis Using PERT Method Consider a project having $10$ activities with the following time estimates: Activity Optimistic $($to$)$ Most Likely $($tm$)$ Pessimistic $($tp$)$ Predecessors A $234-$ B $246$ A C $123$ A D $135$ B E $234$ D F $147$ C and B G $222$ C and B H $258$ F I $135$ F and G J $234$ H and I a$)$ Compute the expected durations and standard deviations for each activity. Use the expected duration and standard deviation formulas: b$)$ Draw the Activity on Node $($AON$)$ and Activity on Arc $($AOA$)$ network representations for this project. c$)$ Determine the earliest start time $($ES$),$ latest start time $($LS$),$ total slack, and free slack for each activity.... Assignment: Cost Estimation and Analysis Exercises for Project Management Exercise $1$: Project Network Analysis Using PERT Method Consider a project having $10$ activities with the following time estimates: $\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|\}\backslash$hline Activity & Optimistic $(\backslash (\backslash$mathbf$\{$t$\}\_\{\backslash$mathbf$\{0\}\}\backslash ))$ & Most Likely $(\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$m$\}\}\backslash ))$ & Pessimistic $(\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash ))$ & Predecessors $\backslash \backslash \backslash$hline A & $2$ & $3$ & $4$ & $-\backslash \backslash \backslash$hline B & $2$ & $4$ & $6$ & A $\backslash \backslash \backslash$hline C & $1$ & $2$ & $3$ & A $\backslash \backslash \backslash$hline D & $1$ & $3$ & $5$ & B $\backslash \backslash \backslash$hline E & $2$ & $3$ & $4$ & D $\backslash \backslash \backslash$hline F & $1$ & $4$ & $7$ & C and B $\backslash \backslash \backslash$hline G & $2$ & $2$ & $2$ & C and B $\backslash \backslash \backslash$hline H & $2$ & $5$ & $8$ & F $\backslash \backslash \backslash$hline I & $1$ & $3$ & $5$ & F and G $\backslash \backslash \backslash$hline J & $2$ & $3$ & $4$ & H and I $\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ a$)$ Compute the expected durations and standard deviations for each activity. Use the expected duration and standard deviation formulas: $\backslash [\backslash$begin$\{$array$\}\{$c$\}$ t$\_\{$e$\}=\backslash$frac$\{$t$\_\{$o$\}+4\backslash$times t$\_\{$m$\}+$t$\_\{$p$\}\}\{6\}\backslash \backslash \backslash$sigma$=\backslash$frac$\{$t$\_\{$p$\}-$t$\_\{$o$\}\}\{6\}\backslash$end$\{$array$\}\backslash ]$ b$)$ Draw the Activity on Node $($AON$)$ and Activity on Arc $($AOA$)$ network representations for this project. c$)$ Determine the earliest start time $($ES$),$ latest start time $($LS$),$ total slack, and free slack for each activity. Deduce the critical path and calculate the probability that the project can be completed within $20$ weeks or less. d$)$ If we want a $\backslash (\backslash$mathbf$\{95\backslash \%\}\backslash )$ probability of completing the project on time, what project completion time should we declare?