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 $7\mathrm{.}2$ $$334\mathrm{.}00$

Atlanta $9\mathrm{.}1$ $$284\mathrm{.}00$

St$.$ Louis $12\mathrm{.}3$ $$314\mathrm{.}00$

Salt Lake City $10\mathrm{.}3$ $$259\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 $$50$ $$57$ $$61$ $$67$ $$64$ $$93$

Atlanta $604763646690$

St$.$ Louis $626555595178$

Salt Lake City $777672624468$

Total Demand $(\backslash$times $1,000$ pounds$)534423934609334409$

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.

Note: Enter your answers in terms of cost per $1,000$ lbs and shipment quantities per $1,000$ lbs$.$ Round your answers to the nearest whole number. Leave the cells blank, whenever zero $(0)$ is required.