Problem $1(14$ pts$)$

Using the cost information below, determine the least expensive way to shorten the project $3$ days. Show your calculations on the network

The table indicates how many days each activity can be crashed and the cost for each day of acceleration.

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

$\backslash$hline Activity & $\backslash$begin$\{$tabular$\}\{$l$\}$

Normal $\backslash \backslash$

Duration

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Cost to $\backslash \backslash$

crash it $\backslash \backslash$

$1$st day

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Cost to $\backslash \backslash$

crash it $\backslash \backslash$

$2$nd day

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Cost to $\backslash \backslash$

Crash it $\backslash \backslash$

$3$rd day

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Cost to $\backslash \backslash$

Crash it $\backslash \backslash$

$4$th day

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Cost to $\backslash \backslash$

Crash it $\backslash \backslash$

$5$th day

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

$\backslash$hline A & $\backslash (\backslash$mathbf$\{12\}\backslash )$ & $800$ & $800$ & $1002\mathrm{.}5$ & $1002\mathrm{.}5$ & $2,100\backslash \backslash$

$\backslash$hline E & $\backslash (\backslash$mathbf$\{7\}\backslash )$ & $650$ & $795$ & n$/$a & n$/$a & n$/$a $\backslash \backslash$

$\backslash$hline F & $\backslash (\backslash$mathbf$\{8\}\backslash )$ & $500$ & $375$ & $375$ & n$/$a & n$/$a $\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{$G$\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )$ & $3,000$ & n$/$a & n$/$a & n$/$a & n$/$a $\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{$H$\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )$ & $4,000$ & $\backslash (\backslash$mathbf$\{$n$\}/\backslash$mathbf$\{$a$\}\backslash )$ & n$/$a & n$/$a & n$/$a $\backslash \backslash$

$\backslash$hline K & $\backslash (\backslash$mathbf$\{5\}\backslash )$ & $2,000$ & $1,000$ & n$/$a & n$/$a & n$/$a $\backslash \backslash$

$\backslash$hline

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

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

$\backslash$hline $1.$ Normal project duration & $\backslash \backslash$

$\backslash$hline $2.$ Activity $/$activities to crash on step $1?$ & $\backslash \backslash$

$\backslash$hline $3.$ Additional cost after step $1?($not cumulative$)$ & $\backslash \backslash$

$\backslash$hline $4.$ Activity$/$activities to crash on step $2?$ & $\backslash \backslash$

$\backslash$hline $5.$ Additional cost after step $2?($not cumulative$)$ & $\backslash \backslash$

$\backslash$hline $6.$ Activity$/$activities to crash on step $3?$ & $\backslash \backslash$

$\backslash$hline $7.$ Additional cost after step $3?($not cumulative$)$ & $\backslash \backslash$

$\backslash$hline

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