A singly reinforced concrete rectangular section is shown in Figure A$1$ with an effective depth, d$=400$mm$.$Given Fc$\text{'}=32$MPa, fsy $=500$MPa. Es $=200,000$MPa.

A$)$ Determine the maximum area of tensile steel reinforcement, Ast that the engineer can design for to ensure an under$-$reinforced section.

B$)$ Determine the maximum ultimate moment capacity for this under$-$reinforced section using the limiting concrete strain criterion of $0\mathrm{.}003.$