calculus
posted by Griffin Bilskie .
A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $5 per square foot and the metal for the sides costs $2 per square foot. Find the dimensions that minimize cost if the box has a volume of 40 cubic feet.

So, the height is 40/x^2
c(x) = 2x^2*5 + 4x(40/x^2)*2
= 10x^2 + 320/x
set the derivative to zero, and you find minimum cost at x = 2∛2
Respond to this Question
Similar Questions

math
A rectangular box with a square base and top is to be made to contain 1250 cubic feet. The material for the base costs 35 cents per square foot, for the top 15 cents per square foot, and for the sides 20 cents per square foot. Find … 
Calculus
A rectangular box with a square base and top is to be made to contain 1250 cubic feet. The material for the base costs 35 cents per square foot, for the top 15 cents per square foot, and for the sides 20 cents per square foot. Find … 
calculus optimization
a company manufactures large cylindrical drums.the bottom and sides are made from a metal that costs $4.00 a square foot, while the reinforced lid costs $6.00 a square foot. ind thedmensions ofa drm that hasa volume of 10cubic feet … 
calculus
A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $2/ft2. The metal for the four rectangular sides costs $3/ft2. Find the dimensions that minimize cost if the box … 
calculus
a rectangular box is to have a square base and a volume of 20 ft cubic if the material for the base costs 30 cent per square foot, the material for the sides cost 10 cent per sqaure foot, and the material for the top costs 20 cents … 
calculus
A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $4 per square foot and the metal for the sides costs $4 per square foot. Find the dimensions that minimize cost … 
Calculus
A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $2 per square foot and the metal for the sides costs $7 per square foot. Find the dimensions that minimize cost … 
Algebra
4. A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.00 per square foot and the material for the top costs $1.50 per square … 
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 … 
Math
A rectangular box is to have a square base and volume of 78 feet cubed. If the material for the base costs $.30 per square feet, the material for the sides costs $.10 per square foot, and the material for the top costs $.20 per square …