Flux control coefficients $($FCC$)(10$ points$)$

Consider the following reaction network:

a$.)$ Calculate flux control coefficients for the pathway flux $J$ from the explicit description of flux in the equation:

$J=v_5^{ss}=e_5{s}_2^{ss}=\frac{(e_2+e_3)e_1[S_0]}{(e_1+e_2+e_3)}$

b$.)$ The flux control coefficients for $e_4$&$e_5$ in the model above are zero. Why?

c$.)$ Verify that for this network: $C_{e_1}^J+C_{e_2}^J+C_{e_3}^J+C_{e_4}^J+C_{e_5}^J=1$