题目内容
湖北省第十四届运动会纪念章委托某专营店销售,每枚进价5元,同时每销售一枚这种纪念章需向荆州筹委会交特许经营管理费2元,预计这种纪念章以每枚20元的价格销售时该店一年可销售2000枚,经过市场调研发现每枚纪念章的销售价格在每枚20元的基础上每减少一元则增加销售400枚,而每增加一元则减少销售100枚,现设每枚纪念章的销售价格为
元,
为整数.
(1)写出该专营店一年内销售这种纪念章所获利润
(元)与每枚纪念章的销售价格
(元)的函数关系式(并写出这个函数的定义域);
(2)当每枚纪念章销售价格
为多少元时,该特许专营店一年内利润
(元)最大,并求出最大值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832736275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832736275.png)
(1)写出该专营店一年内销售这种纪念章所获利润
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832767331.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832736275.png)
(2)当每枚纪念章销售价格
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832736275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832767331.png)
(1)
,定义域为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832845897.png)
(2)当
时,该特许专营店获得的利润最大为32400元.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240258328303176.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832845897.png)
(2)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832861426.png)
试题分析:此题主要考查学生对函数模型在实际问题中应用的能力.(1)在此类问题中要注意单价与销售量之间的相关关系,同时要注意单价价格的取值范围,必要时要进行分段列式,再根据题意求解;(2)经审题实际问题是求函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832767331.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832767331.png)
试题解析:(1)依题意
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240258329082929.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240258329233186.png)
定义域为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832845897.png)
(2)∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240258329553178.png)
∴ 当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832986541.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832861426.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025833001720.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025833017566.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025833033443.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025833048685.png)
综上:当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824025832861426.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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