I. $(10$ points$)$:

A square mat foundation supports the four columns shown.

a$)(7$ points$)$ Determine the magnitude and point of application of the resultant of the four loads.

$($Note: kips $=$ kilo.pounds$).$

b$)(3$ points$)$ Determine the magnitude of the loads that should be applied at points A and $B,$ i$.$e$.F_A$ and $F_B,$ if the resultant of all six loads is to pass through the center of the mat.