For the crushing circuit below, $135$ tons of dry ore feed containing $75\%$ Class $1$ and $35\%$ Class $2$ is

being fed as new feed $($F$)$ to the crushing circuit. The crusher product $($D$)$ is discharged onto the

screen. The screen allows all of class $3$ to go through as undersize circuit product $($P$)$ and $50\%$ of

class $2.$ The rest goes back to the crusher as recycling $($R$).$

Given that there are only three classes with the following size ranges; $($Class $1-80+40cm),($Class $2-$

$40+25cm),$ and $($Class $3-25cm)($For ref purposes use the upper screen i$.$e to calculate $C$ for Class $1,$

used $di=55)$

The Breakage Matrix $(B^{\text{'}}\text{'})$ is given as:

$\left[\begin{array}{ccc}0\mathrm{.}58& 0& 0\\ 0\mathrm{.}38& 0\mathrm{.}59& 0\\ 0\mathrm{.}04& 0\mathrm{.}35& 0\mathrm{.}62\end{array}\right]$

During crushing motion, the maximum opening $K_2$ is always $1\mathrm{.}5x{K}_1,$ the closed setting.

$c_i=1-[\frac{d_i-K_2}{K_1-K_2}{]}^2$

where $C_i$ is the classification function, $K_1$ is the Closed Crusher setting $($CCS$)$ and $K_2,$ the widest

possible opening at a given CCS$.$

$di$ is the particle size.

The overall breakage model with classification function included is as follows;

$d=(I-C)(I-BC{)}^{-1}f$

Note in this case $d$ is the crusher product and $S$ is the screen model which you calculate by applying

the given rules.

Questions:

establish a crusher Closed Side Setting $($CSS$)$ size that will yield a Product $S$ that contains

anywhere between $65$ and $80\%$ Class $3.$

Estimate the energy used by the circuit to produce the product in question $1$ if the work index is

$18\mathrm{.}5.$

If everything stays the same, calculate the product's value without the screen.

Calculate the CSS to obtain the same product as in Q$1,$ but this time without a screen included.

Design a two$-$stage crushing circuit that has both open and closed circuits and briefly comment

on it$.$