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Problem $11-15($Algo$)$

Atlas Corporation is considering a distribution center which will serve three primary market areas: Dallas, Texas; Atlanta, Georgia; and, St$.$ Louis, Missouri. Atlas has determined that the latitude, longitude, and populations of the three metropolitan areas are:

Metropolitan Area Approx.

Latitude Approx.

Longitude Approx.

Population

Atlanta $33\mathrm{.}7584\mathrm{.}396\mathrm{.}5$ million

Dallas $32\mathrm{.}8096\mathrm{.}777\mathrm{.}6$ million

St$.$ Louis $38\mathrm{.}6290\mathrm{.}203\mathrm{.}9$ million

Using the center$-$of$-$gravity method, determine the latitude and longitude of the best location for the distribution center. Use the given population data to estimate demand and enter this data in millions in the necessary calculations $($e$.$g$.,$ enter $5\mathrm{.}4$ million as $"5\mathrm{.}4").($Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$