Allocating observations to test whether two expected values are equal$\mu_{1}-\mu_{2}=\Delta\neq 0?$

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Question:

Suppose that you wish to test the hypothesis $H_{0}:\mu_{1}=\mu_{2}$ versus $H_{1}:\mu_{1}\neq \mu_{2}$,where both variances $\sigma^2_{1}$ and $\sigma^2_{2}$ are know ,A tatal of $n_{1}+n_{2}=N$ observations can be taken.How should these observations be allocated to the two populations to maximize the probability that $H_{0}$ will be rejected if $H_{1}$ is true and $\mu_{1}-\mu_{2}=\Delta\neq 0?$

This is my homework,and I can't find this solution, and I have to turn it in in on Wednesday,so I hope someone can help ,If help me to answer,

I would be very grateful to you

because this homewor is very important to me!

maybe this problem is not easy?

Thank you very much!