Problem $3$: Three columns are supported by a footing. In order to ensure stability of the footing,

the resultant force must fall within the middle third of the footing, known as the

"kern." What are the safe limits for $F_3$ such that the resultant force remains within

the kern? In other words, if $F_3$ is too small, the resultant will be too far to the left.

Likewise, if the magnitude of $F_3$ is too great, the resultant will be too far to the right.

Thus, there is a lower bound and an upper bound for $F_3.$ Any force between will

ensure the resultant is safely located within the kern. Reference all dimensions from

point A$.$