20+ years since I had calculus. I would like to know the dimensions of a box that has the greatest volume in which the L+W+H = 62 inches. If I remember correctly, calculus will solve this for me. This is a practical problem for me.
The maximun volume is from a cube. All three (L, W and H) being equal and 62/3. You lose about 27 cubic inches with 20 by 20 by 22 or about 7 cubic inches with 21 by 21 by 20. You can check other dementions by just multiplying the three values that you are thinking about. The cube is 8826.96 cubic inches.