Minimize the probability:

$\displaystyle P_b=\left(2^{R-B_1log(1+\frac{P_1}{N_1})}-1\right)\left(\frac{N_2B_2}{P_2}\right)$

with respect to the constraint $\displaystyle P=P_1+P_2$

I am trying to solve this using lagrange multipliers.

Even though i got the $\displaystyle \lambda $ value i am not able to find the $\displaystyle P_1 $ and $\displaystyle P_2$ values .

Can anyone please help me to get the $\displaystyle P_1 $ and $\displaystyle P_2$ values .

Thanks