Abox of volume 72 m3 with a square bottom and no top is constructed out of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2 . find the dimensions of the box that minimize total cost.

Square bottom, so L=W
yah

V=HL²

surface area (minus the top) is
SA=2H(2L)+LW
SA=4HL+L²
great
given V=72
72=HL²
solve for H
72/(L²)=H

umm
sorry, I'm all over the place
cost=30(4)HL+40L² or
cost=120HL+40L²
subsitute for H

cost=120(72/(L²))L+40L²
cost=8640/L+40L²
find the minimum using your calculator or take the derivitive
min at L=3∛4≈4.7622031559046

anyway, sub back

72/L²=H
72/((3∛4)²)=H
2∛4=H

the dimentions of the box are
height is 2∛4 or about 3.1748m
length and width are 3∛4 or about 4.7622m

Letter c hope it