The flow diagram of a steady$-$state process for Recovering crystalline potassium chromate $($K$2$Cr$04)$ from an aqueous solution of this salt is shown below:

Four thousand five hundred kilograms per hour of a solution that is $1/3$ K$2$Cr$04$ by mass is combined with a recycle stream containing $36\mathrm{.}4\%$ K$2$Cr$04,$ and the combined stream is fed to an evaporator. The concentrated stream leaving the evaporator contains $49\mathrm{.}4\%$ K$2$Cr$04$; This current enters a crystallizer, where it is cooled $($causing the precipitation of solid K$2$Cr$04$ crystals$)$ and then filtered. The filter cake consists of K$2$Cr$04$ crystals and a solution containing $36\mathrm{.}4\%$ K$2$Cr$04$ by mass; crystals constitute $95\%$ of the total mass of the filter cake. The solution that passes through the filter, also containing $36\mathrm{.}4\%$ K$2$Cr$04,$ is the recycle stream.

Suppose the filtrate were discarded rather than recycled. Calculate the production rate of the crystals. What are the benefits and recycling costs? Solve step by step, without looking at the solver in Felder's mass balance book.