题目内容
已知一企业生产某产品的年固定成本为10万元,每生产千件需另投入2.7万元,设该企业年内共生产此种产品
千件,并且全部销售完,每千件的销售收入为
万元,且![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233110942003.png)
(1)写出年利润
(万元)关于年产品
(千件)的函数解析式;
(2)年产量为多少千件时,该企业生产此产品所获年利润最大?
(注:年利润=年销售收入-年总成本)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311078266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311094447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233110942003.png)
(1)写出年利润
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311125289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311078266.png)
(2)年产量为多少千件时,该企业生产此产品所获年利润最大?
(注:年利润=年销售收入-年总成本)
(1)
;(2)
时,
取最大值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233111412096.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311172380.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311125289.png)
试题分析:本题是实际应用题(1)利用年利润=年销售收入-年总成本及每千件的销售收入
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311094447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311219434.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311234565.png)
试题解析:(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311266477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233112811352.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311297428.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233113121398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233111412096.png)
(2)①当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311266477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311344781.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311172380.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311390579.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311406436.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311422599.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311437427.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311453195.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311172380.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311125289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233115001204.png)
②当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311297428.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240233115311761.png)
当且仅当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311546683.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311578531.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311593594.png)
综合①、②知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311172380.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023311125289.png)
所以当年产量为9千件时,该企业生产此产品获利最大. 12分
![](http://thumb2018.1010pic.com/images/loading.gif)
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