Controlling rate of endothermic reaction

In an experiment, I have two endothermic reactions taking place simultaneously:

\begin{align} \ce{A + B &-> C + D}\tag{1}\\ \ce{E + G &-> Z + F}\tag{2} \end{align}

$$\ce{C}$$ and $$\ce{Z}$$ also take place in a reaction to form the final product of the process $$\ce{J}$$. In my experiment, I have to use a single heating source, and cannot change the concentration of the chemicals in $$\ce{A + B}$$ and $$\ce{E + G}$$ such that the production of $$\ce{J}$$ is as fast as possible. How can I find the optimum temperature for this reaction, and will it be useful?

It is my theory that

$$\frac{\text{rate}_1 + \text{rate}_2}{2}$$

can be found when both reactions take place in water heated by a single source, and the activation energies are known. However, there is a need for another factor other than concentration and heat which needs to ensure that the products $$\ce{C}$$ and $$\ce{Z}$$ are produced at such rates (independently and at different rates) which will ensure an efficient process.

• Usually endothermic reactions don't produce one product out of two reactants. Here you seem to have two such endothermic reaction simultaneously. It is hard to believe. And why is it a zero order reaction ? Please be more explicit ! – Maurice Dec 28 '19 at 12:36
• Do you know quantitatively the kinetics of the reactions involved, and the heats of the reactions?! – Chet Miller Dec 28 '19 at 13:30