名校
解题方法
1 . 某高校为举办百年校庆,需要
氦气用于制作气球装饰校园,化学实验社团主动承担了这一任务.社团已有的设备每天最多可制备氦气
,按计划社团必须在
天内制备完毕.社团成员接到任务后,立即以每天
的速度制备氦气.已知每制备
氦气所需的原料成本为
百元.若氦气日产量不足
,日均额外成本为
(百元);若氦气日产量大于等于
,日均额外成本为
(百元).制备成本由原料成本和额外成本两部分组成.
(1)写出总成本
(百元)关于日产量
的关系式
(2)当社团每天制备多少升氦气时,总成本最少?并求出最低成本.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f504eecdb2ad6ad1bb574617952a8074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8a302092ca2f04f51d20cb6a66856d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4b15e1cf0d684948478bf1ca4cf639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54fef3fe3968e7c106ee83221f17fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50a77242a04a707c5dc728c96aaf053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b94abd222903247775a9be7b9859ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50a77242a04a707c5dc728c96aaf053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264959eda1e8a89c5bd1beef48dcb510.png)
(1)写出总成本
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3539ca060a9d39a6f9866573dc2e5a8.png)
(2)当社团每天制备多少升氦气时,总成本最少?并求出最低成本.
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2022-11-03更新
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760次组卷
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7卷引用:福建省泉州市石狮市第一中学2022-2023学年高一上学期期中考试数学试题