Problem $3$: A beam with a rectangular cross$-$section is subjected to the loading as shown below. There is a uniform distributed load, $q=800\frac{N}{m}$ applied over the entire beam and a concentrated load, $P=25$ kN applied at $a=1$ meter from support A $.$ The allowable bending stress of the material is ${}_{\text{a}\text{l}\text{l}}=7\mathrm{.}0$MPa and the allowable shear stress ${}_{\text{a}\text{l}\text{l}}=0\mathrm{.}75$MPa. If the height, h $,$ of the cross$-$section is $250$ mm $,$ determine the minimum required width, $b,$ of the beam.