Minimizing surface area for open box with square base and 108 in³ volume

[wr1015]

If an open box has a square base and volume of 108 in.³ and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

don't even know where to start on this problem.

 

[whozum]

Find expressions describing the volume and surface area of the box, you want to maximize volume and minimized surface area.

 

[hotvette]

The key is to write what you are given in mathematical terms. For example, you can use V to indicate volume, A to indicate area, x and y to indicate the dimensions of the base and z to indicate the height.

1. Write an equation for V in terms of x, y, z. Hint: what do you know about x & y?

2. Write an equation for A in terms of x, y, z. Hint: the box is open

3. Combining 1 & 2 should give you an expression for A in terms of a single variable

4. You want to minimize A. Hint: in calculus what do you do w/ min/max problems?