Sycamore Plastics $($SP$)$ is a manufacturer of polyethylene plastic pellets used as a

raw material by manufacturers of plastic goods around the U$.$S$.$ 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.

PLANT

MAXIMUM CAPACITY

$(\backslash$times $100,000$ LBS$.)$

PROD. COST

$($PER $1,000$ LBS$.)$

Philadelphia $7\mathrm{.}5$ $$325\mathrm{.}00$

Atlanta $9\mathrm{.}0$ $$275\mathrm{.}00$

St$.$ Louis $12\mathrm{.}0$ $$305\mathrm{.}00$

Salt Lake City $10\mathrm{.}3$ $$250\mathrm{.}00$

SP currently has six contract customers located in New Y