lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllles/editdata.mso"> 06数学建模培训第三阶段题目

06数学建模培训第三阶段题目

要求:两题都做。

A题 降落伞的选择

为向灾区空投救灾物资共2000kg,需选购一些降落伞。已知空投高度为500m,要求降落伞落地时的速度不能超过20m/s。降落伞面为半径r的半球面,用每根长l16根绳索连接着载重m,示意图如图1

 

 

 

 

 

 

 

 

 

 


每个降落伞的价格由3部分组成。伞面价格由半径r决定(见表1);绳索每米为4元,其他费用200元。

降落伞在降落过程中受到空气的阻力,为了确定阻力的大小,用半径3m、载重300kg的降落伞从500m高度作降落试验,测得各时刻的高度(表2)。

试确定降落伞的选购方案,即共需多少个,每个伞的半径多大(在表1中选择),在满足空投要求的条件下,使费用最低。

1

半径r/m

2

2.5

3

3.5

4

费用/

65

170

350

660

1000

 

 

2

t/s

0

3

6

9

12

15

18

21

24

27

30

x/m

500

470

425

372

317

264

215

160

108

55

1

 

 

 

B题 软件开发人员的薪金

一家软件公司的雇员的基本薪金既取决于他们的资历和教育程度,也与他们所负责的工作岗位有关,人事总监希望建立一个薪金与这些因素之间的定量关系,从而对于新聘雇员的底薪做到心中有数。

人事部为研究软件开发人员的薪金与他们的资历、管理水平、教育水平等因素之间的关系,要建立一个数学模型,以便分析公司人事部策略的合理性,并作为新聘用人员薪金的参考。他们认为目前公司人员的薪金总体上是合理的,可以作为建模的依据,于是调查了46名软件开发人员的档案资料,如表1,其中资历一列指从事专业工作的年数,管理水平一列中1表示管理人员,0表示非管理人员,教育水平一列中1表示中学水平,2表示大学水平,3表示研究生水平。


1

编号 

薪金

(元)

资历

(年)

管理水平

教育水平

编号

薪金

(元)

资历

(年)

管理水平

教育水平

01

13876

1

1

1

24

2284

6

1

2

02

11608

1

0

3

25

16978

7

1

1

03

18701

1

1

3

26

14803

8

0

2

04

11283

1

0

2

27

17404

8

1

1

05

11767

1

0

3

28

22184

8

1

3

06

20872

2

1

2

29

13548

8

0

1

07

11772

2

0

2

30

14467

10

0

1

08

10535

2

0

1

31

15942

10

0

2

09

12195

2

0

3