Please solve this problem in full and draw any sketches. Thanks.

A $15$ in$.x26$ in$.$ rectangular reinforced concrete beam supports a factored total uniform load, $w_u=4\mathrm{.}5ki\frac{p}{f}t,$ including the beam's self$-$weight, as shown below. Design the reinforcement required at the supports and the mid span. Use $f_c^{\text{'}}=6,000$ and $f_y=60,000.$ Hint: Two of the three variables known. So$,$ this will be a unique solution.