Influence Lines and Critical loading $(25$ points$)$:

The beam supports a uniform dead load of $500\frac{N}{m}$ and a single live concentrated force of $3000$ N $.$ Assume the support at $A$ is a roller and $B$ is a pin. Draw the influence lines and determine:

$($a$)$ the maximum positive moment at $C$;

$($b$)$ the maximum positive shear at $C.$

Please show all work on a paper!!