Reaction Network

Consider the following reaction in series
     
     E1       E2
A?  B     C
     r1        r2

The two enzymes are E1, E1 and two reaction rates are designated as r1 and r2. The Km, r(max) for E1 and E2 are (1 mM, 3 mM/s) and (0.1mM, 10 mM/s) respectively.

a. Determine the concentration of A and B when the production rate of C is 2 mM/s. Assume the system is a steady state.
b. Now the concentration of A is increased by 3 fold. What is the new production rate of C, What is the new B concentration?
c. Repeat problems a and b for a production rate of C at 0.2mM/s
d. Repeat problems a and b for the case that B is also being used by E3 to make D. The Km and r max for the reaction catalysed by E3 are 0.3 mM and 1 mM/s respectively. What will the effect of changing from conditions in a) to b) on the rate of D synthesis? (i.e. if concentration of A increases 3-fold again from its present concentration, how does the rate of synthesis change?)
e. The above are examples of interactions in reaction network. How cells deal with such “collateral” effect? For example, when the flux of C needs to be reduced, how the cell avoids decreasing the rate of D biosynthesis if D is needed at a constant rate?