a$)$ Create the enrichment operating line equation using the given numerical data and show it on the equilibrium curve,

b$)$ Show the feed line on the equilibrium curve,

c$)$ Determine the ideal number of shelves for the enrichment zone,

d$)$ If the actual number of shelves in the beneficiation zone is $10,$ calculate the column yield,

e$)$ Discuss how the ideal number of shelves will be affected by the change in the reflux rate.