解(1)由于C(n)在各段上都是單調(diào)增函數(shù),因此在每一段上不存在買多于N本書比恰好買n本書所花錢少的問題,一定是在各段分界點附近因單價的差別造成買多于n本書比恰好買n本書所花錢少的現(xiàn)象.
C(25)=11
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25=275,C(23)=12
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23=276,∴C(25)<C(23)……..1分
C(24)=12
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24=288,∴ C(25)<C(24)…………………..…………..2分
C(49)=49
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10=490,C(48)=11
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48=528,∴ C(49)<C(48)
C(47)=11
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47=517,∴ C(49)<C(47)
C(46)=11
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46=506,∴ C(49)<C(46)
C(45)=11
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45=495,∴ C(49)<C(45)……….. ……….………..……..5分
∴這樣的n有23,24,45,46,47,48 …….………..……….. ……………6分
(2)設(shè)甲買n本書,則乙買60-n本,且n
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30,n
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(不妨設(shè)甲買的書少于或等于乙買的書)
①當1
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n
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11時,49
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60-n
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59
出版公司賺得錢數(shù)
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…….. …7分
②當12
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24時,36
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60-
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48,
出版公司賺得錢數(shù)
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③當25
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30時,30
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60-
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35,
出版公司賺得錢數(shù)
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……..……….. ………9分
∴
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……..………………………………..10分
∴當
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時,
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當
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時,
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當
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時,
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…….………. .………. .………. .………...……..12分
故出版公司至少能賺302元,最多能賺384元…….. .………. .……….………..13分