# calculus

posted by .

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 per square foot, determine the dimentions of the box that can be construoted at minimum cost.

• calculus -

let the base be x by x
let the height be y
V = x^2y
20 = x^2y
y = 20/x^2

cost = 30x^2 + 4(10)xy + 20x^2
= 50x^2 + 40x(20/x^2)
= 50x^2 + 800/x

d(cost)/dx = 100x - 800/x^2
= 0 for min cost

100x^3 = 800
x = (8)^(1/3) = 2
y = 20/(2)^2 = 5

check my calculations.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### 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 …
2. ### 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 …
3. ### 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 …
4. ### Calculus

A rectangular box with square base (which is NOT necessarily a cube) and NO top is to be made to contain 9 cubic feet. The material for the base costs \$2 per square foot and the material for the sides \$3 per square foot. Find the dimensions …
5. ### Calculus

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 37¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 13¢/square foot, determine …
6. ### 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 …
7. ### 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 …
8. ### Calculus I

An open box with square base is to be constructed. The material for the base costs \$10 per square foot. The material for the sides costs \$1 per square foot. the box must have an area of 100 square feet. Find the dimensions of the box …
9. ### 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 …
10. ### Math

We need to make an open topped box with a square base and fixed volume of 8 cubic feet. The material for the base costs \$ 6 per square foot and the material for the side costs \$4 per square foot. Write a function for the cost as a …

More Similar Questions