Elemental balances and degree of reduction: An organism $($biomass $=C{H}_{1\mathrm{.}8}{O}_{0\mathrm{.}45}{N}_{0\mathrm{.}16})$ is grown on glycerol $(C{H}_{\frac{8}{3}}O)$ and $N{H}_3$ under aerobic conditions. The overall reaction is as follows:

a$.$ Do you have enough information to solve for all the unknowns $(Y_i)$ and thus balance the reaction? Explain your answer.

b$.$ You are now given an additional constraint: $\frac{Y_{xc}}{Y_x}=0\mathrm{.}8.$ This ratio is called the respiratory quotient, or $RQ,$ which is the number of moles of $C{O}_2$ formed per moles $O_2$ consumed. Solve for the yield coefficients, $Y_j$ in this system and write out the balanced reaction. Use MATLAB $($or another program$).$ Do not solve by hand.

c$.$ Using your results Part $($b$),$ show that the degree of reduction balances for this system.