The compound 1,3-propanediol, which has the structure HO—CH₂—CH₂—CH₂—OH, is a monomer used in the production of polyester fibers and in the manufacture of polyurethanes. 1,3 Propanediol can be produced by chemical processes and also by the fermentation of glycerol in a two-step process using certain bacterial strains. However, neither the chemical nor biological method is well suited for industrial production, because the chemical processes are energy intensive and the biological processes are based on glycerol, an expensive starting material. The DuPont Company has developed a process using a microorganism containing the dehydratase enzyme that can convert other carbon sources, such as carbohydrates or sugars, to 1,3-propanediol. 

a. What is the maximum number of kg of 1,3- propanediol that can be biologically produced from each kg of glycerol, assuming no other energy source is used? What is the stoichiometry of the reaction at the maximum product yield? 

b. What is the maximum number of kg of 1,3- propanediol that can be biologically produced from each kg of glucose, assuming no other energy source is used? What is the stoichiometry of the reaction at the maximum product yield?