问题 解答题
某投资公司计划投资A,B两种金融产品,根据市场调查与预测,A产品的利润y1与投资金额x的函数关系为y1=18-
180
x+10
,B产品的利润y2与投资金额x的函数关系为y2=
x
5
(注:利润与投资金额单位:万元).
(1)该公司已有100万元资金,并全部投入A,B两种产品中,其中x万元资金投入A产品,试把A,B两种产品利润总和表示为x的函数,并写出定义域;
(2)在(1)的条件下,试问:怎样分配这100万元资金,才能使公司获得最大利润?其最大利润为多少万元?
答案

(1)其中x万元资金投入A产品,则剩余的100-x(万元)资金投入B产品,

利润总和f(x)=18-

180
x+10
+
100-x
5
=38-
x
5
-
180
x+10
(x∈[0,100]).…(6分)

(2)∵f(x)=40-

x+10
5
-
180
x+10
,x∈[0,100],

∴由基本不等式得:f(x)≤40-2

36
=28,取等号,当且仅当
x+10
5
=
180
x+10
时,即x=20.…(12分)

答:分别用20万元和80万元资金投资A、B两种金融产品,可以使公司获得最大利润,最大利润为28万元.…(13分)

选择题
完形填空

第二节完型填空(共20小题;每小题1分,满分20分)

阅读下面短文,掌握其大意,然后从36—55各题所给的四个选项(A、B、C和D)中,选出最佳选项

A “Panda Express” plane carrying Mei Lan, three, and Tai Shan, four, landed in Chengdu, where the   36   will join China’s panda – breeding programme.

The pandas were   37  while the two sets of parents were borrowed from China to US zoos. Lent pandas and their young babies must eventually   38   to China.

They both will experience a period of   39   to help themselves deal with the change of language and   40  . Zoo – keepers have advertised for an English – Chinese   41   to teach Mei Lan the Sichuan dialect so that she can understand basic   42  . In Chengdu, mei Lan, from Zoo Atlanta, and Tai Shan, a male from Washington, will have their high – fibre US diet   43   with steamed bread and bamboo shoots.

Since the days of the Cold War China has   44   lent pandas as goodwill gestures, giving rise to the term “panda diplomacy (外交)”. Tai Shan’s   45   will remain at the Smithsonian’s National Zoo in Washington and,   46  , will return to China at the end of their 10 – year loan.

Animal keeper Nicole Meese, who held Tai Shan as a baby, traveled with the animals on the “Panda Express” to China. “Mei Lan was a little   47  , but basically they were both OK,” she said. “I’m going to   48  him terribly.”

She has   49   Tai Shan to understand   50   and prepared a booklet of hand signals to help his new   51   at the Bifengzia Breeding Base in Ya’an, Sichuan.

She was the first baby panda born at Zoo Atlanta, bringing thousands more   52   to the zoo and to its webcam online. And she is expected to stay a media   53  in China: people are being asked to   54   potential mates (配偶) via a website. Superman Kobe and Young Yong, or Doubly Brave, are among the   55  . Experts will also add to more into the choice.

36.A.hosts         B.guests          C.couple         D.pair

37.A.exchanged          B.purchased     C.born         D.raised

38.A.return          B.reflect         C.appeal         D.explain

39.A.recovery      B.adjustment       C.hardships     D.growth

40.A.creature clock  B.climate        C.character      D.food

41.A.school         B.dictionary     C.interpreter     D.teacher

42.A.attitudes      B.commands       C.conditions     D.knowledge

43.A.replaced      B.recycled       C.compared     D.combined

44.A.offered        B.created        C.displayed     D.borrowed

45.A.roommates       B.acquaintances   C.keepers        D.parents

46.A.otherwise     B.therefore      C.too           D.anyway

47.A.curious        B.lonely          C.desperate     D.nervous

48.A.mourn         B.tolerate        C.miss         D.pity

49.A.guaranteed       B.trained         C.expected      D.advised

50.A.gestures       B.movements      C.functions     D.pictures

51.A.colleagues     B.keepers        C.researchers       D.owners

52.A.pandas         B.visitors        C.reporters      D.dollars

53.A.problem      B.phenomenon    C.task          D.star

54.A.suggest        B.select         C.match          D.accuse

55.A.electors       B.partners       C.candidates     D.Employers