ILP Modeling $(20$ marks$)$

A construction company has a limited budget of $\backslash (\backslash$$ $12,000,000\backslash )$ and has access to $21$ project managers to develop a number of construction projects. Each project has its own capital cost requirements, Net Present Value $($NPV$),$ and the number of project managers required $($as shown in the table below$).$ Projects $3$ and $6$ require a given piece of land that only one project can have access to $($the land cannot be shared$).$ In the same way, Projects $4$ and $7$ cannot share the land that each would need. Finally, due to political considerations, Project $5$ will only be completed if and only if Project $2$ is completed. The company would like to decide which project should be completed considering its resource limitations and political considerations. $($DO NOT SOLVE THE MODEL$$

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

$\backslash$hline Project & Project Managers Needed & Estimated Net Present Valus $(1000\backslash$$$)$ & Capital Cost $(1000\backslash$$$)\backslash \backslash$

$\backslash$hline $1$ & $2$ & $2400$ & $1250\backslash \backslash$

$\backslash$hline $2$ & $3$ & $3200$ & $2200\backslash \backslash$

$\backslash$hline $3$ & $1$ & $2200$ & $1700\backslash \backslash$

$\backslash$hline $4$ & $3$ & $4000$ & $2700\backslash \backslash$

$\backslash$hline $5$ & $2$ & $4500$ & $2500\backslash \backslash$

$\backslash$hline $6$ & $5$ & $5000$ & $3200\backslash \backslash$

$\backslash$hline $7$ & $1$ & $3100$ & $1600\backslash \backslash$

$\backslash$hline

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