Posted by kenny on Sunday, November 13, 2011 at 11:54am.
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, Sunday, November 13, 2011 at 12:00pm
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
Answer This Question
Related Questions
 calculus  Melissa wants to make a rectangular box with a square base and cover ...
 Math  You were assigned to construct qn opentop box with a square base from ...
 Calculus  A box with square base and rectangular sides is being designed. The ...
 Math  You were assigned to construct qn opentop box with a square base from ...
 Calculus  dimensions of a box?  A rectangular box with a square bottom and a ...
 calculus  a closed box with square base is to have a V= 2000in^3. The material ...
 precalculus  A company plans to manufacture a container having the shape of a ...
 math  A rectangular box with a volume of 320 cubic units is to be constructed ...
 Calculus  1) A rectangular page is to contain 16 square inches of print. The ...
 calculus  A box is contructed out of two different types of metal. The metal ...
More Related Questions