# calculus

A container with square base, vertical sides, and open top is to be made from 2700 square feet of material. Find the dimensions (length × width × heigth) of the container with greatest volume.

1. 👍 0
2. 👎 0
3. 👁 357
1. volume=s^2*h s is the base length.

but 2700=s^2+4sh
from that, sh=(2700-s^2)/4

then
volume= s(2700-s^2)/4
now, take the derivative of with respect to s...

dV/ds=0=2700/4 -3s^2/4
solve for s

1. 👍 0
2. 👎 0
2. 12X12x14

1. 👍 0
2. 👎 2
posted by bob

## Similar Questions

1. ### Calc 1 (Optomization)

A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs \$6 per square meters and the material for the sides costs \$10 per

asked by Nick on April 6, 2012
2. ### Calculus

A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs \$12 per square meter. Material for the sides costs \$5 per square meter. Find the

asked by John on July 19, 2017
3. ### Calc 1

A rectangular storage container with an open top is to have a volume of 10 m3. The length of the base is twice the width. Material for the base is thicker and costs \$13 per square meter and the material for the sides costs \$10 per

asked by TayB on May 3, 2015
4. ### Calculus

AM having problems understanding what equations to use for this word problem. Please help. A rectangular storage container with an open top is to have a volume of 48ft^3. The length of its base is twice the width. Material for the

asked by Gaby on March 11, 2012
5. ### calculus

Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108ft^2 of sheet steel. (Neglect the thickness of the steel and assume that there is no waste)

asked by Barbara on January 3, 2009
1. ### Calculus

An open top box with a square base is to be made so that it holds 3 cubic feet. Assuming the material on the base costs \$3 per square foot and the material on the sides costs \$2 per square foot, determine the size of the base that

asked by ACDub on April 16, 2014
2. ### pre-calculus

A company plans to manufacture a container having the shape of a right circular cylinder, open at the top, and having a capacity of 24pi cubic inches. If the cost of the material for the bottom is \$.30 per square inch and that for

asked by Nikki on January 23, 2014
3. ### Calculus

A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs \$6 per square meters and the material for the sides costs \$10 per

asked by Joseph on April 9, 2015
4. ### Calculus

I actually have two questions: 4. An open box is to be made from a rectangular piece of material 3m by 2m by cutting a congruent square from each corner and folding up the sides. What are the dimensions of the box of the largest

asked by Anonymous on May 18, 2010
5. ### calculus

A container company is tasked to make an open-top rectangular box with a square base. The box must have a volume of 108cm^(3). let the length of the sides of the square base be x cm and the height h cm. (1) what value of x will

asked by NIKI on August 4, 2011

More Similar Questions