An isothermal reversible reaction a e 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 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 off maximizes the operational profit of the plant? what fraction a fed to the plant is converted at the optimum?