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问题 解答题

某种商品原来定价为每件a元时，每天可售出m件．现在的把定价降低x个百分点（即x%）后，售出数量增加了y个百分点，且每天的销售额是原来的k倍．

（Ⅰ）设y=nx，其中n是大于1的常数，试将k写成x的函数；

（Ⅱ）求销售额最大时x的值（结果可用含n的式子表示）；

（Ⅲ）当n=2时，要使销售额比原来有所增加，求x的取值范围．

答案

（Ⅰ）依题意得

a（1-x%）•m（1+y%）=kam，

将y=nx代入，代简得：

k=-

nx2
10000
+
(n-1)x
100
+1．

（Ⅱ）由（Ⅰ）知当x=

50(n-1)
n
时，k值最大，此时销售额=amk，所以此时销售额也最大．

且销售额最大为

(n+1)2ma
4n
元．

（Ⅲ）当n=2时，k=-

x2
5000
+
1
100
x+1，

要使销售额有所增加，即k＞1．所以

-

x2
5000
+
x
100
＞0，

故x∈（0，50）

这就是说，当销售额有所增加时，降价幅度的范围需要在原价的一半以内．

单项选择题

Few beyond California’ s technology crowd recognise the name Larry Sonsini; none within its circle could fail to. For four decades he has been lawyer, adviser and friend to many prominent companies and investors. Some consider him the most powerful person in Silicon Valley. Companies beg for his law firm to represent them. The 65-year-old chairman of Wilson Sonsini Goodrich & Rosati (WSG&R) has suddenly been thrust into the spotlight: first, for counselling many of the technology firms now under scrutiny for backdating stock options (and in some cases, serving on their boards); and more recently, as outside counsel to Hewlett-Packard (HP), for initially defending the board’s dubious investigative practices.

WSG&R boasts 600 lawyers and represents around half of Silicon Valley’s public companies, including Apple Sun Microsystems and Google. Last year it ranked first in private-equity and venture-capital deals, with nearly twice as many as its closest rival. Over the past five years WSG&R has worked on over 1 000 mergers and acquisitions, collectively worth over $ 260 billion.

The recent troubles cast a shadow over WSG&R’s reputation. Although Mr. Sonsini is not accused of wrongdoing himself, many of his firm’s clients are on the ropes. Former executives at Brocade Communications suffered criminal charges in July, Mr. Sonsini Served on Brocade’s board until last year and his firm was its outside counsel. He also was on the boards of Pixar, Echelon, Lattice Semiconductor, LSI Logic and Novell all firms at which the issuing of stock options is being called into question.

WSG&R dismisses the idea that Mr. Sonsini faced a conflict of interest by acting as both director and legal adviser to so many firms and says he did not advise HP in its investigation of board members. Mr. Sonsini initially said it was "well done and within legal limits". It now seems it was neither.

The phrase "on the ropes" in the second sentence of the third paragraph denotes （）

A. under control

B. in the danger

C. on the horizon

D. on the verge of collapse
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判断题

“整体授信、分配额度”是指利用集团合并会计报表和集团成员各自会计报表分别测算集团整体和成员的授信理论值，根据集团整体风险状况和承贷能力，核定集团客户整体授信额度，同时对集团客户成员进行授信额度分配，并由其分别承贷承还的授信模式。
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