It is desired to crush $100$ ton$/$h of phosphate rock from a feed size whre $80\%$ is less than $4$ in$.$ to a product where $80\%$ is less than $\frac{1}{8}$ in$.$ The work index is $10\mathrm{.}13.$

a$)$ Calculate the power required.

b$)$ Calculate the power require to crush the product further to where $80\%$ is less than $1000mm.$