Determine the lime and soda ash dose, in $m\frac{g}{L}$ as CaO and $N{a}_{2}C{O}_3,$ to soften the water below to a final hardness not to exceed $125m\frac{g}{L}$ as $CaC{O}_3.$ Assume that all the alkalinity is bicarbonate and that the lime is $90\%$ pure. Assume no bypass$/$blending$.$

$\backslash$table$[[$Constituent$,$Concentration as $($:$CaC{O}_3\},$Units$],[$Calcium Hardness,$235\mathrm{.}0,m\frac{g}{L}$ as $CaC{O}_3$