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Li Mengyuan 13122687 Xu Junjie 13122364 Geng Yong 13123949 Ma Yinxiang 13121754

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He won 8 million lottery. He is A’s good friend.

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1. a > b, A will give B the money a. 2. b > a, A will give B the money (b-a)/a. 3. a = b, A will give B the money (a+b).

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There are some interesting things. What should they give figures to make to maximize their own interests ? ?

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The number of B 8million ( ) 4million-8million ( ) 4million ( ) 10w-4million ( ) 10w ( ) 1w-10w ( ) 1w ( ) VOTE 2.Analyze simply.

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If you vote for 8 million. You maybe right in 2 cases. Case 1 : A is a rich man. He didn’t care about the money. Case 2 : A want to give you a test, so he would choose 8 million.

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Then, let’s think about the case that is different from the above 2 cases. So which number is best? ?

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For A: From 1 to 8000000............ Ok ， It’s time to slove the problem. For example : a=50

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For A: From 1 to 8000000............

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Plus all the situations, we get the final formula:

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For B: From 1 to 8000000 For example : b=60..................

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For A: From 1 to 8000000 For example : b=60............ (b+1) (b+2) 7999999 8000000......

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Also ， plus all the situations we get the final formula:

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Derivative ！！！ a ∈【 1 ， 8000000 】 S’(a)>0 So, the function is always increasing. And for A, at 1 will has the minimum expense. We have written down the function S(a) and S(b),but how to deal with them ?

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