题目内容
某种商品原来每件售价为25元,年销售8万件.
(1)据市场调查,若价格每提高1元,销售量将相应减少2000件,要使销售的总收入不低于原收入,该商品每件定价最多为多少元?
(2)为了扩大该商品的影响力,提高年销售量.公司决定明年对该商品进行全面技术革新和营销策略改革,并提高定价到
元.公司拟投入
万元作为技改费用,投入50万元作为固定宣传费用,投入
万元作为浮动宣传费用.试问:当该商品明年的销售量
至少应达到多少万件时,才可能使明年的销售收入不低于原收入与总投入之和?并求出此时商品的每件定价.
(1)据市场调查,若价格每提高1元,销售量将相应减少2000件,要使销售的总收入不低于原收入,该商品每件定价最多为多少元?
(2)为了扩大该商品的影响力,提高年销售量.公司决定明年对该商品进行全面技术革新和营销策略改革,并提高定价到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031213984275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214031724.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046393.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046278.png)
(1)40元;(2)
至少应达到10.2万件,每件定价为30元.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046278.png)
试题分析:(1)这是函数应用题中涉及销售的问题,要清楚知道常识性的等式:销售总收入=销售单价×销售量.提价为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031213984275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214093746.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214124870.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240312141241007.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214140476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214171943.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214187398.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214140476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214218956.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214234459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214249847.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046278.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046278.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214390737.png)
试题解析:(1)设每件定价为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031213984275.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240312141241007.png)
整理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214436703.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214452593.png)
∴要使销售的总收入不低于原收入,每件定价最多为40元. 7′
(2)依题意,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214234459.png)
不等式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240312144991305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214234459.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214249847.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240312145461088.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214702441.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214717530.png)
∴当该商品明年的销售量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031214046278.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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