Please solve this problem entirly and show your work. Also box the answers.A rectangular beam carries uniformly distributed service $($unfactored$)$ dead load of $2\mathrm{.}3ki\frac{p}{f}t.,$

excluding its own self$-$weight $($for lightweight concrete$)$ and $1\mathrm{.}7ki\frac{p}{f}t.$ service $($unfactored$)$ live

loads. Factored concentrated loads of $10$ kip each are placed as shown on the span in addition to

the given distributed loads. Calculate the beam's bending moment capacity and check if it is safe

for bending. The beam width is $15in.,$ and it has a total depth of $30in.$ It has $5-$ #$10$ bars in one

layer. Use $f^{\text{'}}{?}^{\text{'}}=6,000$ and $f_y=60,000.$ Hint: Calculate the bending moment capacity, the

maximum factored bending moment, and then compare for ensuring safety.