$(40$ pts$)$A ground water sample was analyzed with results below:

$C{O}_2=44m\frac{g}{L}$

$C{a}^{2+}=100m\frac{g}{L}$

$M{g}^{2+}=36\mathrm{.}4m\frac{g}{L}$

$N{a}^{+}=46m\frac{g}{L}$

$S{O}_4^{2-}=144\mathrm{.}4m\frac{g}{L}$

$Cl=106\mathrm{.}5m\frac{g}{L}$

Alkalinity $=200m\frac{g}{L}$ as $CaC{O}_3$

$pH=7\mathrm{.}0$

a$)$ Which ion$($s$)$ contribute to hardness? Please determine the hardness of this water sample.

Based on the table below, would you recommend softening?

b$)$ Assume this water sample was taken from a water treatment facility with a capacity of $2$

MGD$.$ Please determine the chemical requirement $($lime$,$ soda and $C{O}_2$ in lbs per day$),$

and sludge production rates $($dry basis, in lbs per day$)$ for lime$-$soda softening.