Given a target reinforcement ratio value $=0\mathrm{.}015,f_c^{\text{'}}=3,000$ psi, $f_y=60,000$ psi, and factored design moment $M_u=200k-$ft to design a doubly reinforced beam section. Calculate reinforcement index, $$; flexural$-$resistance factor, $R,$ and minimum $b{d}^2.$

$=$

$R=$

$b{d}^2,$ in ${?}^3.$