某公司在甲、乙两地同时销售一种品牌车,利润(单位:万元)分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c933f547f521f0fd0a6374b15a833a.png)
和
,其中x为销售量(单位:辆).若该公司本月在这两地一共销售10辆车,求该公司本月获得的最大利润.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c933f547f521f0fd0a6374b15a833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aebf62d230cbee1781de6c1d73a7ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1975501cc3421c250227d90c380ea26.png)
更新时间:2022-11-09 21:02:32
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【推荐1】某工厂生产甲、乙两种产品所得的利润分别为
和
(万元),事先根据相关资料得出它们与投入资金
(万元)的数据分别如下表和图所示:其中已知甲的利润模型为
,乙的利润模型为
.(
为参数,且
).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/cfcb5500-dceb-43f1-a8a6-dd23c25df689.png?resizew=197)
(1)请根据下表与图中数据,分别求出甲、乙两种产品所得的利润与投入资金
(万元)的函数模型
(2)今将
万资金投入生产甲、乙两种产品,并要求对甲、乙两种产品的投入资金都不低于
万元.设对乙种产品投入资金
(万元),并设总利润为
(万元),如何分配投入资金,才能使总利润最大?并求出最大总利润.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7797a8d69d4418fa4f07234d79ea0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7af03463658d2c8e2c95ce3dbd4a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e8a14b5566cab5eb3a6c8cd06c76e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/cfcb5500-dceb-43f1-a8a6-dd23c25df689.png?resizew=197)
(1)请根据下表与图中数据,分别求出甲、乙两种产品所得的利润与投入资金
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)今将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b685c556cc423e4833c1dc671a134cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86608326541db75771f5de9db6187e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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【推荐2】建造一个容积为8
、深为2m的长方体形状的无盖水池,已知池底和池壁的造价分别为120元/
和80元/
,求总造价y(单位:元)关于底面一边长x(单位:m)的函数解析式,并指出该函数的定义域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eab9bcb68861b73f12a65eb9e94700d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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【推荐2】经市场调查,某商场过去18天内,顾客人数
(千人)与时间t(天)的函数关系近似满足
,人均消费
(元)与时间t(天)的函数关系近似满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b224f2ae2453167c0e1813edcf3653.png)
(1)求该商场的日收入
(千元)与时间t(天)
的函数关系式;
(2)求该商场日收入的最小值(千元).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27b234e02e0a1d4d4ffd694744c43ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3466b71d1d9117438ed50388a57d9397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b224f2ae2453167c0e1813edcf3653.png)
(1)求该商场的日收入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8da035ea1123d9f88854da781f2ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da4bf1dc7838403134ecd1261c3cafa.png)
(2)求该商场日收入的最小值(千元).
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