Analysis: Let's assume that the point of sale buys X every day and analyze the meaning of the question. Obviously, when X ∈ [250 250,400], the monthly profit can be the largest. The following is a function of a month's profit, and combined with the monotonicity of the function, you can calculate how much yuan he can earn at most in a month.

Solution: Suppose the point of sale buys X every day,

Obviously, when X ∈ [250 250,400], the monthly profit can be maximized.

So the monthly profit y is

y=20？ 6? 10.50x+ 10？ 6? 10.50? 6? 1250+ 10? 6? 10.08(x-250)-30？ 6? 10.35x

=0.3x+ 1050，x∈[250，400]。

Because the function y is the increasing function in [250,400],

Therefore, when x=400, the maximum value of y is 1 170 yuan.

Answer: Buying 400 points every day can maximize the monthly profit, which means that he can earn at most 1 170 yuan a month.

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