问题 解答题

(12分)

有一种螃蟹,从海上捕获后不放养,最多只能存活两天.如果放养在塘内,可以延长存活时间,但每天也有一定数量的蟹死去.假设放养期内蟹的个体质量基本保持不变,现有一经销商,按市场价收购这种活蟹1000 kg放养在塘内,此时市场价为每千克30元,据测算,此后每千克活蟹的市场价每天可上升1元,但是,放养一天需支出各种费用为400元,且平均每天还有10 kg蟹死去,假定死蟹均于当天全部销售出,售价都是每千克20元.

(1)设x天后每千克活蟹的市场价为p元,写出p关于x的函数关系式;

(2)如果放养x天后将活蟹一次性出售,并记1000 kg蟹的销售总额为Q元,写出Q关于x的函数关系式.

(3)该经销商将这批蟹放养多少天后出售,可获最大利润(利润=Q-收购总额)?

答案

(1)p=30+x

(2)当x=25时,总利润最大,最大利润为6250元

(1)由题意知:p=30+x,

(2)由题意知

活蟹的销售额为(1000-10x)(30+x)元,

死蟹的销售额为200x元.

∴Q=(1000-10x)(30+x)+200x=-10x2+900x+30000.

(3)设总利润为

L=Q-30000-400x=-10x2+500x

=-10(x2-50x) =-10(x-25)2+6250.

当x=25时,总利润最大,最大利润为6250元.

阅读理解

As prices and building costs keep rising, “the do-it-yourself”(DIY)trend(趋势) in the US continues to grow.

“We needed furniture for our living room,” says John Kose, “and we didn’t have enough money to buy it.” So we decided to try making a few tables and chairs. John got married six months ago, and like many young people these days, they are struggling (努力)to make a home when the cost of living is very high. The Koses took a 2-week course for $ 280 at a night school. Now they build all their furniture and make repairs around the house.

Jim Hatfield has three boys and his wife died. He has a full-time job at home as well as in a shoe-making factory. Last month, he received a car repair bill for $420. “I was very upset about it. Now I’ve finished a car repair course. I should be able to fix the car myself. ”

John and Jim are not unusual people. Most families in the country are doing everything they can save money so they can fight the high cost of living. If you want to become a “do-it-yourself”, you can go to DIY classes. And for those who don’t have time to take a course, there are books that tell you how to do things yourself.

小题1:We know from the passage that many people ________ .

A.seldom go to a department store to buy things

B.take DIY courses run by the government

C.like to learn to make their own furniture

D.find it hard to pay for what they need小题2: John and his wife went to evening classes to learn how to _______ .

A.improve the quality of life

B.save time and money

C.make or repair things

D.run a DIY shop小题3:When the writer says that Jim has a full-time job at home, he means Jim ______.

A.keeps house and looks after his children

B.does his own car and home repairs

C.does extra work at night

D.make shoes in his home小题4:Jim Hatfield decided to become a do-it-yourself when ______ .

A.he had to raise the children all by himself

B.he could not possibly do two jobs

C.the car repair class was not helpful

D.his car repairs cost too much小题5:How can people learn DIY? 

A.Go to classes.

B.Read books.

C.Go to classes and read books.

D.The passage doesn’t tell us.

单项选择题