VOOM has four warehouses $1,2,3,$ and $4.$ VOOM needs to supply $200$ Tons to Retailer P$,200$ Tons to Retailer Q$,$ and $200$ tons to Retailer R$.$ The cost of delivery from each warehouse to retailers is provided in the following table. While each warehouse has an inventory of $500$ tons they can supply, $R$ requires that every warehouse supplies at least $25$ tons to $R.$ There is a special arrangement between Warehouse $4$ and $R$ which requires that $W$ arehouse $4$ has. to supply exactly $55$ tons to $R.$ On the other hand, P can take up to $150$ tons each from warehouses I and $2.$

Use linear programming to provide VOOM with a plan to keep their transportation cost minimal.

Delivery cost$/$ton$($$$)$

$\backslash$table$[[$cost$/$ton$($$$),$P$,,1,,R,],[$Warehouse $1,$$$,14\mathrm{.}00,$s$,30\mathrm{.}00,$$$,20\mathrm{.}00],[$Warehouse $2,$$$,30\mathrm{.}00,s,40\mathrm{.}50,$$$,15\mathrm{.}00],[$Warehouse $3,$$$,18\mathrm{.}50,$$$,20\mathrm{.}00,$$$,24\mathrm{.}00],[$Warehouse $4,$$$,15\mathrm{.}50,$s$,12\mathrm{.}50,s,28\mathrm{.}00]]$