I'\" UUICIIIJ. Directions: CHOOSE 3 OF THE PROBLEMS. For each problem, draw a diagram and label it, clearly assign all variables used. Identify the quantity to be maximized or minimized. Conclude your work with a sentence to explain the solution. Each problem is worth 10 points. 1) You have chosen a career in agriculture. Of course, you will need calculus to design the pens for your livestock. You have 720 yards of fencing to create 6 pens of equal area and dimensions. The pens will be designed by dividing a rectangle into 6 pens, as shown below. What should the dimensions of the large rectangular pen be so that the total area is maximized? What is the maximum area of the entire space? What is the maximum area of each pen? E 2) A manufacturer needs to design an open box having a square base and a surface area of 192 square inches. What dimensions will produce a box with a maximum volume? What is the maximum volume? 3) A rectangular poster is to contain 36 square inches of print. There is a margin of 1 inch on all sides of the printed area. What are the dimensions of the poster that will minimize the area of the entire poster? What is that area? 4) You are fencing in a rectanguiar-shaped pen for your dogs. One side of the dog pen will include a 10- foot gate that does not require fencing. (This does not mean that the side of the clog pen is 10 feet long.) You have 150 feet of fencing to use. What are the dimensions that will maximize the area of the dog pen? What is that area