$3-$ The $3\mathrm{.}5m$ long $40cm$ thick cantilever slab shown below is subjected to a live load of $500k\frac{g}{m^2}$ in addition to its dead load and the parapet load of $250k\frac{g}{m}$ at the edge of the slab. Assume concrete grade C$50$ and steel grade S$420,$ assume that all the reinforcement is sufficiently embedded and the distance from outside the bar center is $40mm.$

$($i$)$ Design the reinforcement required such that the maximum expected crack width does not exceed $0\mathrm{.}3mm$ under service load $($no load factors$).$

$($ii$)$ Estimate the long$-$term deflection at the tip.