$1.$ A $40$ ton Pierce$-$Smith convertor working at $90\%$ capacity charged with matte, from the

smelter, with the copper content of $45\%$ and pure oxygen was blown in as the first step of

blowing. A slag was generated by using a low grade ore as the flux. After tapping slag from

the first blow additional matte was charged into the furnace having the same weight as the

FeS which was oxidized in the first blow. Given that the slag compositions are; $30\%$ SiO$2,$

$61\%$ FeO, and $4\%$ CuO $,$ and the flux compositions are; $7\%$ Cu$,15\%$ Fe$,5\%$ S$,$ and $50\%$

SiO$2,$ calculate:

i$)$ The total weight of the flux used and the total weight of the slag produced. $[10]$

ii$)$ The weight of the blister copper formed, assuming it to be as pure Cu$.[10]$