问题 解答题
某酒厂生产A,B两种品牌的酒,每天两种酒共生产700瓶,每种酒每瓶的成本和利润如下表所示,设每天共获利y元,每天生产A种品牌的酒x瓶.
 
A
B
成本(元)
50
35
利润(元)
20
15
(1)请写出y关于x的关系式;
(2)如果该厂每天至少投入成本30000元,那么每天至少获利多少元?
(3)要使每天的利润率最大,应生产A,B两种酒各多少瓶?
答案

(1)y=5x+10500;(2)12335元;(3)A种酒0瓶,B种酒700瓶.

题目分析:(1)根据等量关系:获利y元=A种品牌的酒的获利+B种品牌的酒的获利,即可得到关系式;

(2)关系式为:A种品牌的酒的成本+B种品牌的酒的成本≥30 000,算出x的最小整数值代入(1)即可

(3)关键描述语是:利润率最大,应选取利润率最大的生产最大数量.

(1)根据题意,得y=20x+15(700-x),即y=5x+10500;

(2)根据题意,得50x+35(700-x)≥30000,解得x≥=366

因为x是整数,所以取x=367,代入y=5x+10500,得y=12335

因此每天至少获利12335元;

(3)生产A种酒的利润率为=;生产B种酒的利润率为=

因为<,所以要使每天的利润率最大,应生产A种酒0瓶,B种酒700瓶.

点评:解决本题的关键是读懂题意,根据关键描述语找到符合题意的等量关系和不等关系式组.

单项选择题
填空题

Holidays are special times of (1) from work and other routines. Holidays are often times for celebration, (2) , eating, drinking, travel, and family (3) . In most cultures the scheduling of holidays originally was related to the (4) , the (5) cycle, and (6) . Christmas, December 25, celebrates the (7) of Jesus, but it is not actually known whether Jesus was (8) in the wintertime Over the years Christmas has come to symbolize goodwill and (9) for both Christians and non-Christians, and the (10) of Christmas threatens to replace generosity with greed. Other important holidays in America are Valentine’s Day, St. Patrick’s Day, April Fools’ Day, and (11) . On Valentine’s Day, people give cards, chocolates, flowers, and kisses to their (12) and sweethearts. During Easter Week in late March or early April, Christians remember the death and (13) of Jesus. Although not actually a holiday and has no religious (14) , April Fools’ Day, celebrated on April 1, is a day when people play embarrassing (15) on their fiends and (16) and even on their teachers. In (17) , Labor Day is celebrated on May 1, whereas in (18) and the United States, labor and laborers are honored by a (19) holiday on the first (20) in September.

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