I have a combined likelihood function: $$L(\alpha,\tau)=ce^{-(n+m)\alpha - m\tau}\alpha^{n\bar x}(\alpha+\tau)^{m\bar y} $$
$$ H_0:\tau=0, H_1:\tau\neq0 $$
Construct the test statistics for a maximum likelihood ratio test of $H_0$ versus $H_1$. If $n = 20, \bar x = 100, m = 30 \; and \;\bar y = 105$, use an asymptotic result to carry out the hypothesis test at the 5% significance level.
I am finding it difficult to approach this question and some assistance would be great thank you.