长a宽b深c
S=ab+2bc+2ac
V=abc=8
S=8/c+4/a+4/b
=4/(c/2)+4/a+4/b
=4[1/(c/2)+1/a+1/b)]
(x-y)^2+(y-z)^2+(x-z)^2≥0
x^2+y^2+z^2≥xy+yz+xz
x=y=z时,最小值x^2+y^2+z^2=3x^2
S=4{1/(c/2)+1/a+1/b)≥4[1/√(ac/2)+1/√(bc/2)+1/√ab)
1/(c/2)=1/a=1/b时,S最小=4*3/a=12/a
c/2=a=b时,2a^3=8
a^3=4 a=4^(1/3)
b=4^(1/3) c=2*4^(1/3)
这时用料最省