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 $7\mathrm{.}2$ $$331\mathrm{.}00$

Atlanta $9\mathrm{.}2$ $$281\mathrm{.}00$

St$.$ Louis $12\mathrm{.}2$ $$311\mathrm{.}00$

Salt Lake City $10\mathrm{.}2$ $$256\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 $$49$ $$56$ $$60$ $$66$ $$67$ $$90$

Atlanta $594662636987$

St$.$ Louis $616454585475$

Salt Lake City $767571614765$

Total Demand $(\backslash$times $1,000$ pounds$)531420931606331406$

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.