Posted by kenny on .
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

calculus 
bobpursley,
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= 200s100*1000/s^2=0
200s^3=100,000
s= cuberoot(500)=7.94in
h= 1000/7.94^2=15.9in