We analyze the maximum obtainable yield of B, starting from A in the consecutive chemical reactions A-B-C. We use the temperature as the control variable for a given process duration. We show that all optimal paths start with a branch at infinite temperature and derive a curve on which switching from this temperature to lower temperatures is possible. We also show that the production rate of B at the end of the reaction is equal to the incremental gain of B when the path is re-optimized for increased duration. Finally, we show that for a given set of parameters, there is a unique "maximum useful time" which may be infinite. If a duration longer than this "maximum useful time" is specified, then all reactions should be shut off for. that excess amount of time, a situation that makes most optimization routines become unstable.