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.

PLANT MAXIMUM CAPACITY $(\backslash$times $100,000$ POUNDS$)$ PRODUCT COST $($PER $1,000$ POUNDS$)$

Philadelphia $7\mathrm{.}9$ $$328\mathrm{.}00$

Atlanta $9\mathrm{.}1$ $$278\mathrm{.}00$

St$.$ Louis $12\mathrm{.}1$ $$308\mathrm{.}00$

Salt Lake City $10\mathrm{.}4$ $$253\mathrm{.}00$

SP currently has six contract customers located in New York City; Birmingham, AL; Terre Haute, IN; Dallas, TX; Spokane, WA; and San Diego, CA$.$ Transportation costs between the plants and various customers, as well as contracted demand from each customer, are shown in the table below.

FROM OR TO TRANSPORT COSTS PER $1,000$ POUNDS

NYC BIRMINGHAM TERRE HAUTE DALLAS SPOKANE SAN DIEGO

Philadelphia $$46$ $$53$ $$57$ $$63$ $$74$ $$83$

Atlanta $564359607680$

St$.$ Louis $586151556168$

Salt Lake City $737268585458$

Total Demand $(\backslash$times $1,000$ pounds$)523413923598350398$

Create a solver model and find the optimal solution to help SP develop a distribution plan that will minimize costs to supply the customers$$ demand.