Problem $14-9($Algo$)$

Sycamore Plastics $($SP$)$ is a manufacturer of polyethylene plastic pellets used as a raw material by manufacturers of plastic goods around the United States. SP currently operates four manufacturing centers in Philadelphia, PA; Atlanta, GA; St$.$ Louis, MO; and Salt Lake City, UT$.$ The plants have different capacities and production costs as indicated in the table below.

$\backslash$table$[[$PLANT$,$MAXIMUM CAPACITY,PRODUCT COST $($PER$],[$Philadelphia$,100,000$ POUNDS$),1,000$ POUNDS$)],[$Atlanta$,7\mathrm{.}4,$$$334\mathrm{.}00$