Question: A civil engineer is tasked with designing a reinforced concrete beam to span a distance of $10$ meters between supports. The beam is subjected to a uniformly distributed load of $40$ kN$/$m and two concentrated loads: one at $3$ meters from the left support with a magnitude of $60$ kN$,$ and another at $7$ meters from the left support with a magnitude of $80$ kN$.$ The beam's cross$-$section is rectangular with a width of $300$ mm and an effective depth of $500$ mm$.$ Given that the characteristic compressive strength of concrete is $30$ MPa and the yield strength of the reinforcement is $400$ MPa, perform the necessary calculations to determine the following:

The reactions at the supports.

The maximum bending moment and its location along the span of the beam.