Question

设有一个容积V一定的铝合金盖的圆柱形铁通,已知单位面积铝合金的价格是铁的3倍,问如何设计使总造价最小?

Answer 1

h=桶高

y=总造价

V=r²πh

y=(r²π+2rπh)+3r²π

=4r²π+2V/r

dy/dr=8rπ-2V/r²=0 --> r=(V/(4π))^(1/3)

-->

h=V/(r²π)=[4^(2/3)](V/π)^(1/3)