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Mathematics
Problem
An open-top box with a square base must hold
16,000
cm
3
16{,}000\text{ cm}^3
16
,
000
cm
3
of volume. The base material costs \
0.20
p
e
r
c
m
0.20 per cm
0.20
p
er
c
m
^{2}
,
w
h
i
l
e
t
h
e
m
a
t
e
r
i
a
l
f
o
r
t
h
e
f
o
u
r
s
i
d
e
s
c
o
s
t
s
, while the material for the four sides costs
,
w
hi
l
e
t
h
e
ma
t
er
ia
l
f
or
t
h
e
f
o
u
r
s
i
d
escos
t
s
0.05 per cm
2
^{2}
2
. Determine the length of the base (in centimeters) that minimizes the total material cost.
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