A specialty chemical process uses feedstock S to produce two primary products A and M according to the following stoichiometric reaction:

In the same reactor, a side reaction also takes place in parallel and produces a terminally unrecyclable (tu) component according to the following reaction:

The conversion of S in the aforementioned reactions is virtually complete. The ratio of the rates of reaction of component S in the first and the second reaction is dependent on the temperature according to the following expression:

where and are the reaction rates of the first and second reactions expressed as and is the reaction temperature (in K) which is bounded by the permissible operating range 500<T<600

What is the stoichiometric target for the maximum molar ratio of A&M/tu?

The formulas won't copy over, but they don't really matter. BTHO tu!