Problem $6(20$ points$)$: A statically determinate beam shown below might be subjected to a dead load of $0\mathrm{.}5\frac{k}{f}t$ all over the beams, a live load that consists of a $20-$kip concentrated load and a uniformly live distributed load of $0\mathrm{.}9\frac{k}{f}t$ with a variable length.

a$)$ Draw the influence lines for moment $($M$)$ at section B$.$

b$)$ Compute the maximum positive values of the moment at section $B.$