How to determine whether a single reaction is better than multi-stage reaction?

[zenterix]

Homework Statement

Consider the following reactions

$$\mathrm{2C(s)+2H_2)(g)=2CO(g)+2H_2(g)}$$
$$\mathrm{CO(g)+H_2)(g)=CO_2(g)+H_2(g)}$$
$$\mathrm{CO(g)+3H_2(g)=CH_4(g)+H_2)(g)}$$

and their sum

$$\mathrm{2C(s)+2H_2)(g)=CH_4(g)+CO_2(g)}$$

Relevant Equations

From the standpoint of heat balance, would it be better to develop a process to carry out the overall reactions in three separate reactors or in a single reactor?

The above question is the final part of a problem in Silbey, Alberty, and Bawendi's Physical Chemistry. The main part of the problem had to do with various calculations of changes in enthalpy at 500K, which I completed successfully. The single reaction is endothermic with reaction enthalpy +13.23 kJ.

I'm not sure how to think about the question of if a single reaction is better than the three separate reactions.

What I have thought about so far is the following.

Each separate stage will have unrecoverable energy dissipation.

The multi-stage reaction only has +13.23 kJ of enthalpy change if each reaction occurs and stays at 500K. Lost heat will decrease temperature and so extra energy will be needed to maintain temperature.