$1.(7$ points$)$ 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.

MAXIMUM CAPACITY PROD. COST PLANT $(\backslash$times $100,000$ LBS$.)($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 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.

TRANSPORT COSTS PER $1,000$ LBS$.$

FROM$/$TO NYC BIRMINGHAMTERRE HAUTEDALLASSPOKANESAN DIEGO

Philadelphia $$45$ $$52$ $$56$

$$62$ $$78$ $$85$

Atlanta $554258$

$598082$

St$.$ Louis $576050$

$546570$

$575260$

Total Demand $(\backslash$times $1,000$ lbs$.)$

$525415925$

$600325400$

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. Complete the following tables. $($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.$)$