a rectangular box with a square bottom is to have a volume of 1000 cubic inches. the bottom cost $100 per cubic inch, the sides are $25 per square inch and there is no top. what are the dimensions of the box that has materials costing the least

Answer 1

I bet the bottom is 100/in^2, not cubic.

size of box: s^2 * h s is side dimention on bottom.

cost= 100*s^2+ 4*25sh

but h= 1000/s^2

cost= 100s^2+100s(1000/s^2)

dcost/ds= 200s-100*1000/s^2=0

200s^3=100,000
s= cuberoot(500)=7.94in
h= 1000/7.94^2=15.9in