$5.(23$ marks$)$ The beam is fixed to the wall at A and supported by a deformable post having a diameter of $50$ min at B$.$ The post and the beam are made of the same material having a Young's modulus of E$-200$ GPa. The beam has a constant moment of inertia N A $=3\mathrm{.}0$ x $10-4$m$4$ about its neutral axis. With the applied loads shown below, determine $($i$)$ the support reactions at A and B; $($ii$)$ the deflection at point B; and $($iii$)$ the slope and the deflection at point C on the beam.