问题 解答题
某工厂计划生产A、B两种产品共10件,其生产成本和利润如下表:
 
A种产品
B种产品
成本(万元/件)
2
5
利润(万元/件)
1
3
(1)若工厂计划获利14万元,问A、B两种产品应分别生产多少件?
(2)若工厂计划投入资金不多于44万元,且获利多于14万元,问工厂有哪几种生产方案?
(3)在(2)的条件下,哪种生产方案获利最大?并求出最大利润。
答案

(1)A种产品8件,B种产品2件(2)有6种方案:生产A产品2件,B产品8件; A产品3件, B产品7件;A产品4件, B产品6件;A产品5件,B产品5件;A产品6件,B产品4件;A产品7件,B产品3件。(3)生产A产品2件、B产品8件时 ,可获得最大利润16万元

解:(1)设生产A种产品x件,则生产B种产品10-x件,根据题意,得

x+3(10-x)=14,解得,x=8。

则10-x=10-8=2。

∴应生产A种产品8件,B种产品2件。

(2)设应生产A种产品x件,则生产B种产品有10-x件,根据题意,得

,解得:2≤x<8。

∴可以采用的方案有6种方案:生产A产品2件,B产品8件; A产品3件, B产

品7件;A产品4件, B产品6件;A产品5件,B产品5件;A产品6件,B产品4件;A产品7件,B产品3件。

(3)设生产A种产品x件时,利润为z万元,根据题意,得

z=x·1+(10-x)·3=-2x+30,

∵-2<0,∴随着x的增大,z减小。

∴当x=2时,z最大,最大利润z=-2×2+30=26。

所以当生产A产品2件、B产品8件时 ,可获得最大利润16万元。

(1)设生产A种产品x件,则生产B种产品有10-x件,根据计划获利14万元,即两种产品共获利14万元,即可列方程求解。

(2)根据计划投入资金不多于44万元,且获利多于14万元,这两个不等关系即可列出不等式组,求得x的范围,再根据x是非负整数,确定x的值,x的值的个数就是方案的个数。

(3)由已知列出函数关系式,由一次函数的性质即可求解。

单项选择题 B型题
阅读理解

“When I grow up, I want to be...”

Almost all of us have thought about, or been asked to think about, our future careers. Our answers may differ greatly. Even now your aspirations may have changed from when you were in primary school.

However, it seems career options aren’t only based on personal taste. In a survey carried out by Teens, doctors, lawyers, and bankers were some of most popular careers that people said they hoped to follow. This is in line with a similar survey carried out in the UK in May 2011 by job website monster. Co.uk, in which medicine was the top choice among UK teenagers aged between 13 and 17.

Medicine and law are two of the oldest and best known professions. Their prestige (威望) may come from the fact that doctors and lawyers are some of the most esteemed members of society, and they make good money. Joining these high-profile professions is often seen as a sign of upward social mobility.

It is equally unsurprising that banking is now one of the most common career choices. Youngsters worldwide think of banking and see the money rolling in. Wealth is increasingly becoming one of the most important indicators of a successful career. British young men list the UK tycoon Alan Sugar, Microsoft founder Bill Gates and Facebook chief Mark Zuckerberg as their top role models “for their wealth”. Just as Chinese teenagers see being a banker as a good and fun pathway to “wealth”.

However, not every child has the makings of doctor, lawyer, or banker. They are those who see fulfillment and happiness in other areas, and many teenagers dare to ink more individuality into their career options. As the Teens’ survey discovered, a variety of unconventional jobs---coffee shop owner, gourmet(美食家),waiter at a fast food restaurant---are among teenagers’ career choices. They can be equally interesting and rewarding jobs.

With every choice comes responsibility and challenge, and all career paths require specific education and training, you have to learn to balance optimism and confidence with being realistic about your particular talents and skills.

小题1:What is the passage mainly about?

A.Careers in teenagers’ mind.

B.Choosing a good job is very important.

C.Teenagers in the UK like doctors.

D.The choice of career needs challenge.小题2:What is the top career choice among UK teenagers aged between 13 and 17 according to the article?

A.Medicine

B.Law

C.Bank

D.Education小题3:According to the article, all of the following are the benefits of being a doctor except_______.

A.respect from others

B.the oldest profession

C.high pay

D.upward social mobility.小题4:What do youngsters think is increasingly becoming one of the most important indicators of a successful career?

A.Prestige

B.Fulfillment

C.Happiness

D.Wealth小题5:What can we learn from the last paragraph?

A.According to your particular talents and skills, you can choose your favorite career.

B.Specific education and training can help get a good job.

C.Whatever career you choose, you should balance optimism and confidence with being realistic about your particular talents and skills.

D.Responsibility is the most important when you choose a good job.