Deriving the equation for S* for competitive product inhibition.

Problem Statement:
Derive the equation for S* for competitive product inhibiton.  

Definition of variables:
S* = the surface substrate concentration at steady state.  (For plug flow reactor);

Sb = bulk substrate conc;
Ks = mass transfer coeff;
Ki = competitive inhibition rate constant;
Km = substrate conc that give 1/2 max enzyme reaction rate;
Vmax = max specific growth rate;
V= specific growth rate;