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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