Using data below, develop a model that can determine how many tons of wheat to transport from each grain elevator to each mill on a monthly basis?

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

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

Grain $\backslash \backslash$

Elevator

$\backslash$end$\{$tabular$\}$ & Supply & Mill & Demand $\backslash \backslash$

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

$1.$ Kansas $\backslash \backslash$

City

$\backslash$end$\{$tabular$\}$ & $350$ & A$.$Chicago & $220\backslash \backslash$

$\backslash$hline $2.$ Omaha & $250$ & B$.$St$.$Louis & $100\backslash \backslash$

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

$3.$ Des $\backslash \backslash$

Moines

$\backslash$end$\{$tabular$\}$ & $500$ & C$.$Cincinnati & $300\backslash \backslash$

$\backslash$hline Total & $1000$ tons & Total & $600$ tons $\backslash \backslash$

$\backslash$hline

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

Transport Cost from Grain Elevator to Mill $(\backslash$$$/$ton$)$

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

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

Grain $\backslash \backslash$

Elevator

$\backslash$end$\{$tabular$\}$ & $\backslash$multicolumn$\{1\}\{|$c$|\}\{$ A$.$Chicago $\}$ & B$.$St$.$ Louis & C$.$Cincinnati $\backslash \backslash$

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

$1.$ Kansas $\backslash \backslash$

City

$\backslash$end$\{$tabular$\}$ & $\backslash (\backslash$$ $6\backslash )$ & $\backslash (\backslash$$ $8\backslash )$ & $\backslash (\backslash$$ $10\backslash )\backslash \backslash$

$\backslash$hline $2.$ Omaha & $7$ & $11$ & $11\backslash \backslash$

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

$3.$ Des $\backslash \backslash$

Moines

$\backslash$end$\{$tabular$\}$ & $4$ & $5$ & $12\backslash \backslash$

$\backslash$hline

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

$1)$ Formulate the LP model $($complete formulation no need for solution$)$

$2)$ If we need to enhance the model so that we can decide on which Grain Elevator to select for supplies, what needs to be done for the model $($show full details$).$