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In this video tutorial, we aim to solve an open box optimization problem using a thin piece of cardboard measuring 10 inches by 10 inches. The objective is to determine the dimensions that will result in a box with maximum volume. The first step is to find the objective function, which in this case is the volume of the box. By visualizing the problem and cutting out squares at the corners of the cardboard, we can better represent the objective function in terms of a single variable to simplify the optimization process.