Web Reference: Oct 28, 2024 · In the following example, we look at constructing a box of least surface area with a prescribed volume. It is not difficult to show that for a closed-top box, by symmetry, among all boxes with a specified volume, a cube will have the smallest surface area. 4.7.1 Set up and solve optimization problems in several applied fields. One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In applied optimization problems, particularly in packaging design, one common task is to maximize the volume of a box. For instance, consider a box with an open top created by cutting equal-sized squares from the corners of a 3-foot by 8-foot rectangular sheet of cardboard and folding up the sides.
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