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我市“上品”房地产开发公司于2010年5月份完工一商品房小区，6月初开始销售，其中6月的销售单价为0.7万元/m2，7月的销售单价为0.72万元/m2，且每月销售价格y1（单位：万元/m2）与月份x（6≤x≤11，x为整数）之间满足一次函数关系：每月的销售面积为y2（单位：m2），其中y2=-2000x+26000（6≤x≤11，x为整数）．

（1）求y1与月份x的函数关系式；

（2）6～11月中，哪一个月的销售额最高？最高销售额为多少万元？

（3）2010年11月时，因会受到即将实行的“国八条”和房产税政策的影响，该公司销售部预计12月份的销售面积会在11月销售面积基础上减少20a%，于是决定将12月份的销售价格在11月的基础上增加a%，该计划顺利完成．为了尽快收回资金，2011年1月公司进行降价促销，该月销售额为（1500+600a）万元．这样12月、1月的销售额共为4618.4万元，请根据以上条件求出a的值为多少？

答案

（1）设y1=kx+b（k≠0），

由题意

6k+b=0.7
7k+b=0.72

解得：

k=0.02
b=0.58
∴y1=0.02x+0.58．

（2）设第x个月的销售额为W万元，

则W=y1y2=（0.02x+0.58）（-2000x+26000）

=-40x2-640x+15080，

∴对称轴为直线x=-

b
2a
=-
-640
-80
=-8，

∵当6≤x≤11是W随x的增大而减小，

∴当x=6时，

Wmax=-40×62-640×6+15080=9800（6分）

∴6月份的销售额最大为9800万元．

（3）11月的销售面积为：-2000×11+26000=4000（m2）

11月份的销售价格为：0.02×11+0.58=0.8（万元/m2）

由题意得：4000（1-20a%）×0.8（1+a%）+1500+600a=4618.4，

化简得：4a2+5a-51=0，解得：a1=3，a2=-

17
4
（舍）

∴a=3．

单项选择题

船舶国籍证书的有效期为（）年。

A、3

B、5

C、10
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