Question

An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?

Answer 1

I made several boxes with different sized square bases, such as 1x1, 2x2, 3x3, 4x4, 5x5, and 6x6. I calculated the heights of all of them, being 120, 30, 13.333, 7.5, 4.8, and 3.333 respectively. By using the $2/sq. in. for the sides and $3/sq. in. for the square base, I found that the box with the dimensions: 5x5x4.8 produced the most minimal cost at $267:

(5x4.8)x4 = 96 sq. in. x 2 = $192
5x5 = 25 sq. in. x 3 =$75

$192 + $75 = $267