Using the Warehouse Location Information that has been provided, apply the weighted center of gravity approach to determine the appropriate location for a new distribution facility if one is to be built. Round your final coordinates $($X$,$ Y$)$ to two decimal places. Also, provide a separate discussion of other relevant factors that would influence the choice of a specific location once the $($X$,$Y$)$ coordinates have been identified. Here is the information given about location The company would also like to assess whether its current warehouse location is appropriate based on where customers are located. For each of the key markets served by Throx, the table below indicates FY$2021$ estimated population figures and X and Y coordinates of the market locations. $($These figures have been rounded for ease of computation.$)$ Sales of Throx products in each location is roughly proportional to the size of the population.

Population

LA $-$ Long Beach $12,900,000,$ San Francisco $-$ Oakland $4,600,000,$ San Diego $3,300,000,$ Sacramento $2,400,000$

X

LA $-$ Long Beach $34,$ San Francisco $-$ Oakland $38,$ San Diego $33,$ Sacramento $39$

Y

LA $-$ Long Beach $118,$ San Francisco $122,$ San Diego $117,$ Sacramento $121$