Consider the following reaction scheme in which A can react forming two products P$1$ and P$2$:

A $$ I$1$ k$1,$ k$-1$

I$1->$ P$1$ k$2$

I$1$ I$2$ k$3,$ k$-3$

I$2->$ P$1$ k$4$

I$2->$ P$2$ k$5$

Using the steady$-$state approximation $($with I$1$and I$2$ considered as intermediates$),$ derive the rate

expressions for the formation of two products P$1$ and P$2$ in terms of the given rate constants. Derive the

expression for the product branching ratios in this reaction