Question $2(12$ marks$)$

$2\mathrm{.}1$ After blowing a $100$ ton LD converter for $20$ minutes, the blown metal analysis was; $0\mathrm{.}05\%$ C$,0\mathrm{.}20\%$ Mn$.$ Calculate the amount of ferromanganese needed to raise Mn to $0\mathrm{.}80\%$ given FeMn contains $66\%$ Mn and costs R$12,000$ per ton. $[6]$

$2\mathrm{.}2$ If after blowing for only $15$ minutes, Mn in blown metal is $0\mathrm{.}45\%,$ calculate the saving in ferromanganese by interrupting the blow after $15$ minutes $[6]$