Problem #1-Maximizing Volume: The Box: Four squares of equal sizes are cut out of the four corners of a piece of 10-inch by 13-inch construction paper. The sides are then folded up and secured so as to make an open box. Your objective is to create the box with the maximum possible volume. Step 1: Build the objective function. Let x denote the length of the sides of the squares you cut out of the corners of the paper. Build the function V(x) that calculates the volume of the box as a function of the length of the sides of the squares you cut out. Draw a diagram if it helps Step 2: Find the critical values. Using the derivative, find the critical values of the volume function Step 3: Classify critical values. Perform an appropriate test to classify the critical value(s) from Step 2. Step 4: Answer the question. What is the length of the sides of the squared you should cut out in order to create the box with maximum possible volume? What is the maximum possible volume?