$(25$pts$)$ A W$24$x$55$ beam made from A$36$ alloy steel and is loaded as shown. The beam's cross section is oriented such that deflection will be resisted by $1xc(x-x$ axis$).$

a$.$ What is the maximum deflection at the left end of the beam in units of inch, caused by the $30$kip point load only? Give answer to $4$ significant figures.

b$.$ What is the maximum deflection at the left end of the beam in units of inch, caused by the $25ki\frac{p}{f}t$ triangular distributed load only? Give answer to $4$ significant figures.

c$.$ Using superposition, what is the maximum deflection at the left end of the beam in units of inch? Give answer to $4$ significant figures.