A Manufacturer of Cat Towers Wishes to Locate a Super

A manufacturer of cat towers wishes to locate a super assembly facility to meet their cat tower assembly needs for the next millennium. Currently, carpet, cylinders, yarn and fasteners are purchased in bulk from suppliers in North Haverbrook, Ogden, and Springfield in the quantities shown in the table. The super assembly facility would ship to distribution centers located in Seattle, Lubbock, Nashville, and Philadelphia. The locations of all of these cities on an x-y grid, transportation costs on a ton per mile basis, and total tonnage are all contained in the table. Formulate and solve a model that will minimize the shipping costs to the super assembly center.
$\begin{array} { | l | c | c | c | c | } \hline \text { Sources/Markets } & \begin{array} { c } \text { Transportation } \\\text { Cost } \$ / \text { ton mile } \\\left( \mathbf { F } _ { \mathbf { n } } \right)\end{array} & \begin{array} { c } \text { Quantity } \\\text { in Tons } \\\left( \mathrm { D } _ { \mathbf { n } } \right)\end{array} & \mathbf { X } _ { \mathbf { n } } & \mathbf { Y } _ { \mathbf { n } } \\\hline \text { Supply } & & & & \\\hline \text { North Haverbrook } & 1.1 & 650 & 700 & 1200 \\\hline \text { Ogden } & 1.2 & 450 & 250 & 600 \\\hline \text { Springfield } & 1.4 & 400 & 225 & 825 \\\hline \text { Market } & & & & \\\hline \text { Seattle } & 2.25 & 300 & 50 & 1200 \\\hline \text { Lubbock } & 2.25 & 200 & 450 & 300 \\\hline \text { Nashville } & 2.25 & 500 & 800 & 250 \\\hline \text { Philadelphia } & 2.25 & 500 & 950 & 1100 \\\hline\end{array}$
Where should the new plant be located and what is the total system shipping cost?