(Solved): A piece of cardboard that is 10 inches by 15 inches is being made into a box without a top. To do ...

A piece of cardboard that is 10 inches by 15 inches is being made into a box without a top. To do so, squares are cut from each corner of the box and the remaining sides are folded up. If the box needs to be at least 1 inch deep, and no more than 3 inches deep: 1. Draw a labeled diagram that shows the given information. Let x be the variable we introduce to represent the choice we make in creating the box. Label the diagram appropriately. 2. Determine a formula for the function V(x) that tells us the volume of the box. 3. What is the domain of the function V? That is, what values of x make sense for input? Are there additional restrictions provided in the problem? 4. Determine all critical numbers of the function V. 5. Evaluate V at each of the endpoints of the domain and at any critical numbers that lie in the domain. 6. What is the maximum possible volume of the box? the minimum?