A beam with a rectangular cross$-$section has a uniformly distributed load applied over two$-$thirds of its length and a concentrated load applied at the end C$,$ as shown in Figure $9\mathrm{.}1.$ The beam is simply supported at B$.$

$($a$)$ Using superposition, Calculate the reaction forces at A and B$.$

$($b$)$ Draw the shear force and bending moment diagram for the beam.

Please provide a drawn diagram and finalized answers.

Figure $9\mathrm{.}1$