Web Reference: May 26, 2020 · Use the extrema to answer the question being asked. With these steps in mind, let’s work through a typical applied optimization example. Keep in mind, there are many different kinds of applied optimization problems, but we solve all of them using this same set of steps. 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. Consequently, we consider the modified problem of determining which open-topped box with a specified volume has the smallest surface area. In this activity, students will work on a famous math problem exploring the volume of an open box. The aim is to create an open box (without a lid) with the maximum volume by cutting identical squares from each corner of a rectangular card.
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