Problem$)(20$ points$)$

Todd's Direct, a major TV sales chain headquartered in New Orleans, is about to open its first

outlet in Mobile, Alabama, and wants to select a site that will place the new outlet in the center of

Mobile's population base. Todd examines the seven census tracts in Mobile, plots the coordinates

of the center of each from a map, and looks up the population base in each to use as a weighting.

The information gathered appears in the following table.

a$)$ At what center$-$of$-$gravity coordinates should the new store be located?

b$)$ Census tracts $103$ and $105$ are each projected to grow by $40\%$ in the next year. How will this

influence the new store's coordinates?