Problem $4$

For the project in Problem $2,$ normal time $($in days$)$ and normal cost $(\backslash$$$),$ and crash time $($in days$)$ and crash cost $(\backslash (\backslash$$ $\backslash ))$ is given for each task as follows:

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

$\backslash$hline TASK & DESCRIPTION & $\backslash$begin$\{$tabular$\}\{$c$\}$

NORMAL $\backslash \backslash$

TIME

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

NORMAL $\backslash \backslash$

COST

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

CRASH $\backslash \backslash$

TIME

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

CRASH $\backslash \backslash$

COST

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

$\backslash$hline A & Inspect the house & $4$ & $400$ & $2$ & $1000\backslash \backslash$

$\backslash$hline B & Appraise the house & $3$ & $300$ & $1$ & $1100\backslash \backslash$

$\backslash$hline C & Do the title search & $4$ & $400$ & $3$ & $600\backslash \backslash$

$\backslash$hline D & Get the tax clearance & $5$ & $500$ & $3$ & $900\backslash \backslash$

$\backslash$hline E & Get the sales permit & $2$ & $200$ & $1$ & $250\backslash \backslash$

$\backslash$hline F & Find a buyer & $21$ & $3000$ & $7$ & $8000\backslash \backslash$

$\backslash$hline G & Get a mortgage & $14$ & $2000$ & $7$ & $4000\backslash \backslash$

$\backslash$hline H & Get the legal documents & $10$ & $500$ & $5$ & $1000\backslash \backslash$

$\backslash$hline I & File the legal documents & $1$ & $100$ & $1$ & $100\backslash \backslash$

$\backslash$hline J & Final closing & $1$ & $100$ & $1$ & $100\backslash \backslash$

$\backslash$hline

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

a$.$ Formulate an appropriate crashing model to achieve a completion time of $30$ days or less.

$(10$ points$)$

b$.$ Use Excel QM to determine which tasks should be shortened to achieve this goal and by how much? $(8$ points$)$

c$.$ How much will it cost to achieve this goal? $(4$ points$)$