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. $\begin{array} { | l | c | c | c | c | }
\hline \text { Sources/Markets } & \begin{array} { c }
\text { Transportation } \
\text { Cost } \$ / \text { ton mile } \
\left( \mathbf { F } _ { \mathbf { n } } \right)
\end{array} & \begin{array} { c }
\text { Quantity } \
\text { in Tons } \
\left( \mathrm { D } _ { \mathbf { n } } \right)
\end{array} & \mathbf { X } _ { \mathbf { n } } & \mathbf { Y } _ { \mathbf { n } } \
\hline \text { Supply } & & & & \
\hline \text { North Haverbrook } & 1.1 & 650 & 700 & 1200 \
\hline \text { Ogden } & 1.2 & 450 & 250 & 600 \
\hline \text { Springfield } & 1.4 & 400 & 225 & 825 \
\hline \text { Market } & & & & \
\hline \text { Seattle } & 2.25 & 300 & 50 & 1200 \
\hline \text { Lubbock } & 2.25 & 200 & 450 & 300 \
\hline \text { Nashville } & 2.25 & 500 & 800 & 250 \
\hline \text { Philadelphia } & 2.25 & 500 & 950 & 1100 \
\hline
\end{array}$
-What is the distance between the Ogden and Seattle locations?
A) 450 miles
B) 350 miles
C) 630 miles
D) 1050 miles

Question

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. $\begin{array} { | l | c | c | c | c | } 
\hline \text { Sources/Markets } & \begin{array} { c } 
\text { Transportation } \
\text { Cost } \$ / \text { ton mile } \
\left( \mathbf { F } _ { \mathbf { n } } \right)
\end{array} & \begin{array} { c } 
\text { Quantity } \
\text { in Tons } \
\left( \mathrm { D } _ { \mathbf { n } } \right)
\end{array} & \mathbf { X } _ { \mathbf { n } } & \mathbf { Y } _ { \mathbf { n } } \
\hline \text { Supply } & & & & \
\hline \text { North Haverbrook } & 1.1 & 650 & 700 & 1200 \
\hline \text { Ogden } & 1.2 & 450 & 250 & 600 \
\hline \text { Springfield } & 1.4 & 400 & 225 & 825 \
\hline \text { Market } & & & & \
\hline \text { Seattle } & 2.25 & 300 & 50 & 1200 \
\hline \text { Lubbock } & 2.25 & 200 & 450 & 300 \
\hline \text { Nashville } & 2.25 & 500 & 800 & 250 \
\hline \text { Philadelphia } & 2.25 & 500 & 950 & 1100 \
\hline
\end{array}$
-What is the distance between the Ogden and Seattle locations?
A) 450 miles
B) 350 miles
C) 630 miles
D) 1050 miles

Quizplus · Accepted Answer

The distance between two points on an x-y grid can be calculated using the distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For Ogden (250, 600) and Seattle (50, 1200), the distance is $\sqrt{(50 - 250)^2 + (1200 - 600)^2} = \sqrt{(-200)^2 + (600)^2} = \sqrt{40000 + 360000} = \sqrt{400000} = 632.46$ miles, which rounds to 630 miles.

A Manufacturer of Cat Towers Wishes to Locate a Super