Problem $1$: $(20$ points$)$

Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload $($in hundreds of dollars$),$ supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago and from Tampa to Boston:

A

B

C

D

$\backslash$begin$\{$tabular$\}\{$llccccc$\}$

$\backslash$hline & & $\backslash$multicolumn$\{4\}\{$c$\}\{$ To $($cost$,$ in $\backslash (\backslash$mathbf$\{\backslash$$ $100\}\backslash )$ s$)\}$ & $\backslash \backslash$

$\backslash$cline $\{2-6\}$ & & New York & Philadelphia & Chicago & Boston & Supply $\backslash \backslash$

$\backslash$cline $\{2-6\}\backslash (\backslash$mathbf$\{1\}\backslash )$ & Tampa & $\backslash (\backslash$$ $9\backslash )$ & $\backslash (\backslash$$ $14\backslash )$ & $\backslash (\backslash$$ $12\backslash )$ & $\backslash (\backslash$$ $17\backslash )$ & $200\backslash \backslash$

$\backslash (\backslash$mathbf$\{2\}\backslash )$ & Miami & $11$ & $10$ & $6$ & $10$ & $200\backslash \backslash$

$\backslash (\backslash$mathbf$\{3\}\backslash )$ & Fresno & $12$ & $8$ & $15$ & $7$ & $200\backslash \backslash$

$\backslash$hline & Demand & $130$ & $170$ & $100$ & $150$ & $\backslash \backslash$

$\backslash$hline

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

$1-$ Formulate this problem as a linear programming model. $(15$ points$)$

$2-$ Provide a feasible solution. $(5$ points$)$