PLEASE DO NOT JUST COPY ANOTHER CHEGG SOLUTION THEY ARE INCORRECT

An isothermal reversible reaction A B is carried out in an aqueous solution. The reaction is first-order in both directions. The forward rate constant is 0.4 h and the equilibrium constant is 4.0. The feed to the plant contains 100 kg/m of A and enters at the rate of 12 m /h. Reactor effluents pass to a separator, where B is completely recovered. The reactor is a stirred tank of volume 60 m . A fraction, f , of the unreacted effluent is recycled

as a solution containing 100 kg/m of A and the remainder is discarded. Product B is worth $2 per kilogram and operating costs are $50 per cubic meter of solution entering the separator. What value of f maximizes the operational profit of the plant? What fraction A fed to the plant is converted at the optimum?