2. Find the dimensions of a box with largest vol- ume formed from a 10-inch by 10-inch piece of cardboard cut and folded as shown below. 10 X end X X I X - - top 10 bottom top front end front - X - - X end3. You have 120 feet of fencing to construct a pen with four equal-sized stalls. If the pen is rectangular and shaped like the one shown below, what are the dimensions of the pen of largest area and what is that area? 9. You are a lifeguard standing at the edge of the water when you notice a swimmer in trouble (see figure below) 40 m out in the water from a point 60 m down the beach. Assuming you can run at a speed of 8 meters per second and swim at a rate of 2 meters per second, how far along the Shore should you run before diving into the wa- ter in order to reach the swimmer as quickly as possible? you 60 m .'. _________ : 3' w \\ X \\\\ \\ - 40 in v? \\ \\ \\ \\ \\ swimmer