P$1.$ For the beam with supports as given below, draw influence lines for $($a$)$ the vertical reaction at $B,($b$)$ the shear at $C,$ and $($c$)$ the moment at C$.$

P$2.$ For the same beam given in P$1,$ show that the magnitude of the influence lines for $($a$),($b$),$ and $($c$)$ match the corresponding reactions or internal forces you would get at these points if a unit load was applied at $E($i$.$e$.,$ if a unit load is applied at $E,$ what is the corresponding vertical reaction at $B,$ shear at $C,$ and moment at $C?$ Do these values match the magnitude of your influence lines at $E?)$

P$3.$ For the same beam given in P$1,($a$)$ where should a single concentrated force and a uniformly distributed load be applied to produce the maximum positive reaction at B$,$ positive maximum shear at $C,$ and positive maximum moment at $C?($b$)$ if the concentrated force has a magnitude of $5$ kips $,$ and the uniformly distributed load has a magnitude of $500lb\frac{f}{f}t,$ what would be the resulting maximum positive reaction at $B,$ positive maximum shear at $C,$ and positive maximum moment at C $?$