Element potential method of equilibrium

• For the element potential method, how many equations and unknowns are there for a general hydrocarbon burning in air?
• We are minimizing Gibbs free energy, but subject to what constraints?
• What is the method used when minimizing a function subject to contraints?
• True or False: the method reduces to minimizing element potentials, which are linear combinations of chemical (species) potentials.
• Outline the basic steps of the element potential method.
• What is the approach used to find an initial guess for the element potentials ($\lambda_k$) from some initial composition?
• Suppose you have equilibrium at a given enthalpy (e.g., adiabatic from some initial temperature and composition). How could you solve that problem using the equilibrium methods at a given known temperature?