Bean Oil Problem: A certain kind of bean contains an oil that has commercial value. On average, the beans contain $14wt\%$ bean oil. The following continuous process is used to extract the oil. The beans are first crushed and then mixed with hexane in an extractor. Essentially all the oil in the beans dissolves in the hexane. The residue of crushed bean solids mixed with the solution of oil in hexane passes through a filter which produces a filtrate and a filter cake. The filter cake is $75\%$ bean solids and leaves the process as a discard. The filtrate contains no solids. It passes to an evaporator which removes the hexane as a vapour and leaves the bean oil as a liquid. The bean oil contains no hexane and leaves the process as the final product. The hexane vapour is first condensed and then recycled back to the extractor where it is used again to extract oil from cushed beans. To make up for losses of hexane from the process, fresh hexane is continually added to the extractor along with the recycled hexane. The total flow rate of hexane to the extractor is carefully controlled to be $3\mathrm{.}5$ times the flow rate of crushed beans.

Calculate

a$)$ The bean oil production $($product flow rate$)$ per kg of beans processed. b$)$ The amount of fresh hexane required per $kg$ of beans processed.

c$)$ The ratio of the flow rate of fresh and recycled hexane.