QUESTION $3[30$ points$].$ Grove Orthopedics, a physician specialty group in central Virginia, is in the process of assessing the feasibility of opening an orthopedic specialty hospital in the Greater Richmond area. Its first consideration is the geographic placement of the facility. In order to determine a central location for the hospital, the project team has collected the coordinates of hospitals in the area and their associated total number of annual joint replacement surgeries, shown in Table below.

$\backslash$table$[[,$Coordinates,$],[$Hospital$,x,y,$Annual Surgery Volume$],[$St$.$ Francis Medical Center,$37\mathrm{.}467034,77\mathrm{.}658739,127],[$Memorial Regional Medical Center,$37\mathrm{.}629101,37\mathrm{.}629101,285],[$St$.$ Mary's Hospital of Richmond,$37\mathrm{.}583740,77\mathrm{.}512423,159],[$Johnston$-$Willis Hospital,$37\mathrm{.}510447,77\mathrm{.}595307,494],[$Columbia$/$HCA John Randolph,$37\mathrm{.}307383,77\mathrm{.}291447,36],[$Chippenham Hospital,$37\mathrm{.}515562,77\mathrm{.}525947,90],[$Henrico Doctors,$37\mathrm{.}604585,77\mathrm{.}541493,90],[$Parham Doctors,$37\mathrm{.}632049,77\mathrm{.}525464,90]]$

$3.$a$.$ Determine the location for a new orthopedic specialty hospital using the center of gravity method.

$3.$b$.$ Determine the location for a new orthopedic specialty hospital using the weighted center of gravity method.