This is Math in the Modern World. Kindly write the answer on a piece of paper for us to easily understand thankyou

TEST YOURSELF In the following exercises, set up and evaluate each optimization problem. 1. To carry a suitcase on an airplane, the length + width + height of the box must be less than or equal to 62 in. Assuming the height is fixed, show that the maximum volume is V = h(31 -3h) . What height allows you to have the largest volume? 2. You are constructing a cardboard box with the dimensions 2 m by 4 m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions of the box with the largest volume? 3. Find two positive integers such that their sum is 10 , and minimize and maximize the sum of their squares. 4. You have 400ft of fencing to construct a rectangular pen for cattle. What are the dimensions of the pen that maximize the area? You can run at a speed of 6 mph and swim at a speed of 3 mph and are located on the shore, 4 miles east of an island that is 1 mile north of the shoreline. How far should you run west to minimize the time needed to reach the island