2010数学建模竞赛才C题

参考文献

【1】陆宜清，高等数学，河南： 郑州大学出版社，2007。

【2】韩中庚，数学建模竞赛——获奖论文精选与点评，北京： 科学出版社，2007。

【3】王兵团，数学建模基础， 北京：清华大学出版社和北京交通大学出版社， 2004。

【4】姜启源，数学模型，北京：高等教育出版社，1995。. 【5】叶其孝，大学生数学建模竞赛辅导教材（四），长沙：湖南教育出版社，2001

【6】周义仓，赫孝良，数学建模实验，西安：西安交通大学出版社，2001 【7】王沫然，MATLAB 6.0与科学计算，电子工业出版社，2001

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附录

问题二（方案三） 公司一（21） >>

f=7.2*(x^2+(y-5)^2)^0.5+7.2*y+7.2*((x-15)^2+(y-z)^2)^0.5+28.2*(25+(8-z)^2)^0.5 f =

36/5*(x^2+(y-5)^2)^(1/2)+36/5*y+36/5*((x-15)^2+(y-z)^2)^(1/2)+141/5*(25+(8-z)^2)^(1/2)

>> diff(f,'x') ans =

36/5/(x^2+(y-5)^2)^(1/2)*x+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*x-30)

>> diff(f,'y') ans =

18/5/(x^2+(y-5)^2)^(1/2)*(2*y-10)+36/5+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*y-2*z)

>> diff(f,'z') ans =

18/5/((x-15)^2+(y-z)^2)^(1/2)*(-2*y+2*z)+141/10/(25+(8-z)^2)^(1/2)*(-16+2*z) >>

[x,y,z]=solve('36/5/(x^2+(y-5)^2)^(1/2)*x+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*x-30)=0','18/5/(x^2+(y-5)^2)^(1/2)*(2*y-10)+36/5+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*y-2*z)=0','18/5/((x-15)^2+(y-z)^2)^(1/2)*(-2*y+2*z)+141/10/(25+(8-z)^2)^(1/2)*(-16+2*z)=0')

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x =

36791/540250*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+1861137696/586981625-26751/54025*3^(1/2)-160506/117396325*2173^(1/2)+2173/1080500*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3 y =

13/2-5/2*3^(1/2)-15/2173*2173^(1/2) z =

451757/54025-2173/324150*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3-6519/108050*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+17834/10805*3^(1/2)+107004/23479265*2173^(1/2) >>

x=36791/540250*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+1861137696/586981625-26751/54025*3^(1/2)-160506/117396325*2173^(1/2)+2173/1080500*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3 x =

5.4593

>> y=13/2-5/2*3^(1/2)-15/2173*2173^(1/2) y =

1.8481 >>

z=451757/54025-2173/324150*(-3+5*3^(1/2)+30/2173*2173^(1/2))^3-6519/108050*(-3+5*3^(1/2)+30/2173*2173^(1/2))^2+17834/10805*3^(1/2)+107004/23479265*2173^(1/2) z =

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7.3564 >>

7.2*(x^2+(y-5)^2)^0.5+7.2*y+7.2*((x-15)^2+(y-z)^2)^0.5+28.2*(25+(8-z)^2)^0.5

ans =

280.1771

公司二（24）

>> syms x y z f >>

f=7.2*(x^2+(y-5)^2)^0.5+7.2*y+7.2*((x-15)^2+(y-z)^2)^0.5+31.2*(25+(8-z)^2)^0.5 f =

36/5*(x^2+(y-5)^2)^(1/2)+36/5*y+36/5*((x-15)^2+(y-z)^2)^(1/2)+156/5*(25+(8-z)^2)^(1/2)

>> diff(f,'x') ans =

36/5/(x^2+(y-5)^2)^(1/2)*x+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*x-30)

>> diff(f,'y') ans =

18/5/(x^2+(y-5)^2)^(1/2)*(2*y-10)+36/5+18/5/((x-15)^2+(y-z)^2)^(1/2)*(2*y-2*z)

>> diff(f,'z') ans =

18/5/((x-15)^2+(y-z)^2)^(1/2)*(-2*y+2*z)+78/5/(25+(8-z)^2)^(1/2)*(-16+2*z)

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