问题 解答题

我区的某公司,用1800万元购得某种产品的生产技术、生产设备,进行该产品的生产加工,已知生产这种产品每件还需成本费40元.经过市场调研发现:该产品的销售单价,需定在100元到200元之间为合理.当单价在100元时,销售量为20万件,当销售单价超过100元,但不超过200元时,每件新产品的销售价格每增加10元,年销售量将减少1万件;设销售单价为x(元),年销售量为y(万件),年获利为W(万元).

(年利润=年销售总额-生产成本-投资成本)

(1)直接写出y与x之间的函数关系式;

(2)求第一年的年获利W与x之间的函数关系式,并请说明不论销售单价定为多少,该公司投资的第一年肯定是亏损的,最小亏损是少?

(3)在使第一年亏损最小的前提下,若该公司希望到第二年的年底,弥补第一年的亏损后,两年的总盈利为1490万元,且使产品销售量最大,销售单价应定为多少元?

答案

(1)y=20-

x-100
10
=-0.1x+30;

(2)W=(x-40)(-0.1x+30)-1800

=-0.1x2+34x-3000

=-0.1(x-170)2-110…(5分)

∵不论x取何值,-0.1(x-170)2≤0,

∴W=-0.1(x-170)2-110<0,

即:不论销售单价定为多少,该公司投资的第一年肯定是亏损 

∵100<x≤200

∴当x=170时,第一年最少亏损110万元.

(3)依题意得

(x-40)(-0.1x+30)-110=1490  

解之得x1=140   x2=200  

∵k=-0.1<0,∴y随x增大而减小,

∴要使销量最大,售价要最低,即x=140元;

阅读理解

阅读理解。

     Mr. Hunt came from a poor family. He had three brothers and two sisters. His father worked

hard but wasn't paid much. And his mother did all the housework at home. They were both able

but they couldn't get enough money for their family.

     Mr. Hunt was in school for only three years and he had to stop to help his parents though he

was good at his lessons. When he was sixteen, he came to the city and began to work in a small

factory. He learned from an old worker and became a skilled worker. The old worker liked him

and married his daughter to him. The young man did not have his own house and had to live with his

parents-in-law. His mother-in-law always thought he was poor and often chattered. So the young

man tried to save everything and hoped to have his own house.

      It was one fine Sunday. The old woman wanted to have a picnic on the top of the hill. She told

Mr. Hunt to drive her car. But sometimes she told him to turn left and sometimes to turn right. The

young man had to listen to her. At a crossing the lights were red but she made him turn left. The

policeman stopped them and told the young man to give his license to him.

     "If I did wrong, sir," said Mr. Hunt, "It was my mother-in-law's fault (过错). She was driving the

car though she sat behind me!"

1. The Hunts were poor because ____.

A. they were lazy

B. they were too weak to work

C. they couldn't make enough money

D. they weren't able enough

2. Mr. Hunt left the school because ____.

A. he didn't like studying

B. his family was poor

C. he wasn't clever

D. he hoped to stay at home

3. ____, so the old man married his daughter to him.

A. Mr. Hunt became a skilled worker

B. Mr. Hunt was friendly to him

C. Mr. Hunt was paid much in the factory

D. Mr. Hunt worked for six years there

4. The old woman was ____ to Mr. Hunt.

A. good

B. bad

C. friendly

D. useless

5. Which of the following is wrong?

A. The old woman herself drove the car that day.

B. It was the old woman's fault.

C. Mr. Hunt hated his mother-in-law.

D. The old woman told Mr. Hunt to run the red lights.

单项选择题