A simply supported beam ABCD carries a uniformly distributed load of $2\mathrm{.}0k\frac{N}{m}$ between A and $B,$ point loads of $5kN$ and $6kN$ at $B$ and $C$ respectively, and a uniformly distributed load of $7\mathrm{.}0k\frac{N}{m}$ between $B$ and $D$ as shown below.

a$)$ Determine the deflection at the mid$-$span of the beam

b$)$ Determine the value and location of the maximum bending moment.

c$)$ Under the $6kN$ point load

d$)$ If $El$ is $1{10}^{5}kN{m}^2$ comment on whether the beam is acceptable for an allowable deflection of $\frac{L}{250}.$