Question

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.35 per square foot, the material for the sides costs $0.10 per square foot, and the material for the top costs $0.15 per square foot, determine the dimensions of the box that can be constructed at minimum cost.

Answer 1

let the length of the base be x
let the height be h
then the volume \(V= l*w*h = x^2h\)

the are of the top and bottom of the base are each is x^2
the are of the 4 sides is 4xh
so all together we get
cost \(C=.35x^2+.15x^2+.1*4xh\)
we know h = V/x^2 = 20x^2
plug that in
\(C = .35x^2+.15x^2+.1*4x(20/x^2) = .35x^2+.15x^2+.1*4(20/x)\)

Answer 2

can you handle it from here?

Answer 3

@Vane11 ?

Answer 4

that should say we know h = V/x^2 = 20/x^2

Answer 5

I think I can let me try and take it from here, I'll let you know if I get stuck, thanks!

Answer 6

got it, 2, 2, and 5, Thanks again!

Answer 7

sounds right