Both Saccharomyces cerevisiae yeast and Zymomonas mobilis bacteria produce etanol from glucose under anaerobic conditions without external electron acceptors. The biomass yield from glucose is $0\mathrm{.}11g{g}^{-1}$ for yeast and $0\mathrm{.}05g{g}^{-1}$ for $Z.$ mobilis. In both cases the nitrogen source is $N{H}_3.$ Both cell compositions are represented by the formula $C{H}_{1\mathrm{.}8}{O}_{0\mathrm{.}5}{N}_{0\mathrm{.}2}.$

a$)$ What is the yield of etanol from glucose in both cases? Use Matlab to solve the elemental balance.

b$)$ How do the yields calculated in $($a$)$ compare with the thermodynamic m$$ximum$?$