问题 解答题

某商场试销一种成本为每件60元的服装,规定试销期间销售单价不低于成本单价,且获利不得高于45%,经试销发现,销售量y(件)与销售单价x(元)符合一次函数y=kx+b,且x=65时,y=55;x=75时,y=45.

(1)求一次函数y=kx+b的表达式;

(2)若该商场获得利润为W元,试写出利润W与销售单价x之间的关系式;销售单价定为多少元时,商场可获得最大利润,最大利润是多少元?

(3)若该商场获得利润不低于500元,试确定销售单价x的范围.

答案

解:(1)根据题意得

解得k=﹣1,b=120.

所求一次函数的表达式为y=﹣x+120.

(2)W=(x﹣60)(﹣x+120)=﹣x2+180x﹣7200=﹣(x﹣90)2+900,

∵抛物线的开口向下,

∴当x<90时,W随x的增大而增大,而销售单价不低于成本单价,且获利不得高于45%,即60≤x≤60×(1+45%),

∴60≤x≤87,

∴当x=87时,W=﹣(87﹣90)2+900=891.

∴当销售单价定为87元时,商场可获得最大利润,最大利润是891元.

(3)由W≥500,得500≤﹣x2+180x﹣7200,

整理得,x2﹣180x+7700?0,

而方程x2﹣180x+7700=0的解为 x1=70,x2=110.

即x1=70,x2=110时利润为500元,

而函数y=﹣x2+180x﹣7200的开口向下,

所以要使该商场获得利润不低于500元,销售单价应在70元到110元之间,

而60元/件≤x≤87元/件,

所以,销售单价x的范围是70元/件≤x≤87元/件.

阅读理解

Early to bed and early to rise makes a man healthy, wealthy and wise.

This is an old English saying (谚语). It means that we should go to bed early at night and get up early in the morning. If we do, we shall be healthy. We shall also be rich and clever.

Is this true? Perhaps it is. The body must have enough sleep. Children of your age need ten hours’ sleep every night. If you go to bed late, you can’t have enough sleep. Then you can’t think carefully and your homework will be wrong. You will not be wise and you may not become wealthy!

Some people go to bed late at night and get up late in the morning. This is not good for them. We should sleep at night when it is dark. The dark helps us sleep well. When the daylight comes, we should get up. This is the time for exercise. If the body is not used, it will become weak. Exercise keeps it strong.

Exercise helps the blood (血液) to move around inside the body. Blood takes nutrition (营养) to all parts of our bodies. The brains (大脑) in our heads also need blood. We think with our brains. If we keep our bodies healthy, and take exercise, we can think better!

Our bodies also need air to breathe (呼吸). Without air we will die. Get up early in the morning and we can have plenty of clean, fresh air. That will keep us healthy and happy.

根据短文内容,选择正确答案。

小题1:The old English saying tells us _______.

A.how to make more money

B.when we should get up

C.it is important to go to bed and get up early

D.to stay up late小题2:A child needs at least _______ hours’ sleep every night.

A.7

B.8

C.9

D.10小题3:If you want to make your body strong, you should _______.

A.exercise often

B.have enough sleep

C.go to bed early

D.get up early小题4:_______ provides nutrition for our brains.

A.Air

B.Blood

C.Exercise

D.Sleep小题5:Which of the following statements is Not true?

A.Enough sleep makes you think carefully.

B.The more sleep you have, the cleverer you are.

C.Dark is good for sleeping.

D.People will die without air.

单项选择题 A1/A2型题