3. A standard piece of printer paper has a perimeter of 39 inches. A standard sized...

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3. A standard piece of printer paper has a perimeter of 39 inches. A standard sized piece of paper has dimensions of 8.5 inches by 11 inches, but does this maximize the area of the paper? Your goal is to find the dimensions of a piece of paper (a rectangle) that maximizes the area with a specified perimeter. a. Draw and label a picture, then write the function that you need to maximize. b. Your constraint is the 39-inch perimeter. Write the constraint equation in terms of the variables in the picture you drew in part a. c. Use the method of Lagrange multipliers to find the dimensions that maximize the area. d. What is the maximum area? 3. A standard piece of printer paper has a perimeter of 39 inches. A standard sized piece of paper has dimensions of 8.5 inches by 11 inches, but does this maximize the area of the paper? Your goal is to find the dimensions of a piece of paper (a rectangle) that maximizes the area with a specified perimeter. a. Draw and label a picture, then write the function that you need to maximize. b. Your constraint is the 39-inch perimeter. Write the constraint equation in terms of the variables in the picture you drew in part a. c. Use the method of Lagrange multipliers to find the dimensions that maximize the area. d. What is the maximum area?