问题 解答题
清明过后,第四届重庆渝北玉峰山樱桃节将隆重启幕,届时市民可游览玉峰山、采摘樱桃果、观赏精彩文艺演出,参与这场以樱桃为主题的春日盛会.为指导今年的樱桃销售,津南果品批发公司在樱桃节前夕,对往年的市场销售情况进行了调查统计,得到如下数据:
销售价x(元/千克)28262522
日销售量y(千克)500150020003500
(1)请观察表格中的数据,用所学过的一次函数、反比例函数或二次函数的知识,求出日销售量y(千克)与销售价x(元/千克)之间的函数关系式;
(2)经过与果农商洽,津南果品批发公司确定今年的樱桃进价为13元/千克,试求当销售价定为多少时,可以使日销售利润最大?最大日销售利润是多少元?
(3)由于今年天气适宜,加上果农精心种植、科学管理,樱桃在3月中旬提前上市,很受市民欢迎.津南果品批发公司在(2)问前提下,即取得最大日销售利润的销售价基础上将价格提高了2a%,结果日销售量反而增加了3a%,持续一周后,随着樱桃的大量上市,公司决定将价格在取得最大日销售利润的销售价基础上下调a%,预计日销售量与第一周持平.这样,在第二周销售结束后,除去各种杂费30800元,预计两周总销售利润可达585200元.请参看以下数据,估算a的整数值.
(参看数据:
696
≈26.38
697
≈26.40
698
≈26.42
699
≈26.44
答案

(1)设y=kx+b,当x=25时,y=2000,x=26时,y=1500,

25k+b=2000
26k+b=1500

解得:

k=-500
b=14500

则y=-500x+14500;

经验证,表格中其余各组数据均符合此函数;

(2)设日销售利润为W元,则W=(x-13)(-500x+14500)=-500(x-21) 2+32000,

当x=21时,W最大=32000,

答:当销售价定为21时,可以使日销售利润最大利润32000元;

(3)当x=21时,代入y=-500x+14500=-500×21+14500=4000,

则7×[21(1+2a%)-13]×4000(1+3a%)+7[21(1-a%)-13]×400(1+3a%)-30800=585200,

∴(8+42a%)(1+3a%)+(8-21a%)(1+3a%)=22,

∴(16+21a%)(1+3a%)=22,

设a%=t,则21t 2+23t-2=0,

∵△=23 2+8×21=697>0,

∴t=

-23±
697
42

∵t>0,

∴t=

-23+
697
42

∴a=100t=100×

-23+
697
42
≈100×
-23+26.4
42
≈8.

阅读理解

阅读理解。

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