QUESTION THREE

$[20]$

The table below provides the duration estimates in days for a construction project.

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

$\backslash$hline Activity & Predecessor & Optimistic Time & Most Likely Time & $\backslash$begin$\{$tabular$\}\{$l$\}$

Pessimistic $\backslash \backslash$

Time

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

$\backslash$hline A & $-$ & $4$ & $7$ & $10\backslash \backslash$

$\backslash$hline B & $-$ & $2$ & $9$ & $10\backslash \backslash$

$\backslash$hline C & A$,$B & $2$ & $5$ & $8\backslash \backslash$

$\backslash$hline D & C & $16$ & $19$ & $28\backslash \backslash$

$\backslash$hline E & C & $6$ & $9$ & $24\backslash \backslash$

$\backslash$hline F & E & $1$ & $7$ & $13\backslash \backslash$

$\backslash$hline

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

$2$

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

$\backslash$hline G & C & $4$ & $10$ & $28\backslash \backslash$

$\backslash$hline H & D$,$F & $2$ & $5$ & $14\backslash \backslash$

$\backslash$hline I & G$,$F & $5$ & $8$ & $17\backslash \backslash$

$\backslash$hline J & H$,$I & $2$ & $5$ & $8\backslash \backslash$

$\backslash$hline

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

$3\mathrm{.}1$ Determine the expected completion time for each activity.

$(5)3\mathrm{.}2$ Complete the table below by filling in the missing values. You are not required to show the network diagram in your answer sheet. Simply write $4\mathrm{.}2\mathrm{.}1$ to $4\mathrm{.}2\mathrm{.}10$ and insert the missing values on your answer sheet

$(10)$

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

$\backslash$hline Activity & Duration & ES & LS & EF & LF & SLACK $\backslash \backslash$

$\backslash$hline A & $7$ & $0$ & $1$ & $4\mathrm{.}1\mathrm{.}1$ & $8$ & $1\backslash \backslash$

$\backslash$hline B & $8$ & $0$ & $0$ & $8$ & $8$ & $0\backslash \backslash$

$\backslash$hline C & $5$ & $8$ & $4\mathrm{.}1\mathrm{.}2$ & $13$ & $13$ & $4\mathrm{.}1\mathrm{.}3\backslash \backslash$

$\backslash$hline D & $20$ & $13$ & $14$ & $33$ & $4\mathrm{.}1\mathrm{.}4$ & $1\backslash \backslash$

$\backslash$hline E & $11$ & $4\mathrm{.}1\mathrm{.}5$ & $13$ & $24$ & $24$ & $0\backslash \backslash$

$\backslash$hline F & $7$ & $24$ & $24$ & $31$ & $4\mathrm{.}1\mathrm{.}6$ & $0\backslash \backslash$

$\backslash$hline G & $12$ & $13$ & $19$ & $25$ & $31$ & $4\mathrm{.}1\mathrm{.}7\backslash \backslash$

$\backslash$hline H & $6$ & $33$ & $34$ & $4\mathrm{.}1\mathrm{.}8$ & $40$ & $4\mathrm{.}1\mathrm{.}9\backslash \backslash$

$\backslash$hline I & $9$ & $31$ & $31$ & $40$ & $40$ & $0\backslash \backslash$

$\backslash$hline J & $5$ & $40$ & $40$ & $45$ & $4\mathrm{.}1\mathrm{.}10$ & $0\backslash \backslash$

$\backslash$hline

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

$3\mathrm{.}3$ What do you understand about the term $"$ critical path" and determine the critical path and its duration for the project