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,outbound transportation costs on a ton per mile basis,and total tonnage are all contained in the table. $$\begin{array} { | l | c | c | c | c | } \hline \text { Sources/Markets } & \begin{array} { c } \text { Transportation Cost } \\\$ \text { /ton mile } \left( F _ { \mathrm { n } } \right) \end{array} & \begin{array} { c } \text { Quantity in } \\\text { Tons } \left( \mathrm { D } _ { \mathrm { n } } \right) \end{array} & \mathrm { X } _ { \mathrm { n } } & \mathrm { Y } _ { \mathrm { n } } \\\hline \text { Supply } & & & & \\\hline \text { North Haverbrook } & 1.1 & 650 & 700 & 1200 \\\hline \text { Ogden } & 1.2 & 450 & 250 & 600 \\\hline \text { Springfield } & 1.4 & 400 & 225 & 825 \\\hline \text { Market } & & & & \\\hline \text { Seattle } & 2.25 & 300 & 50 & 1200 \\\hline \text { Lubbock } & 2.25 & 200 & 450 & 300 \\\hline \text { Nashville } & 2.25 & 500 & 800 & 250 \\\hline \text { Philadelphia } & 2.25 & 500 & 950 & 1100 \\\hline\end{array}$$ What is the minimal shipping cost that satisfies all market demand?

A) $2,546,632
B) $2,586,342
C) $2,451,668
D) $2,522,982