Let A be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in a form that does not include the length of the side parallel to the barn. Aequals nothing (Type an expression.) The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To maximize the area of the pen, the sides perpendicular to the barn should be nothing m long and the side parallel to the barn should be nothing m long. (Type exact answers, using radicals as needed.) b. Let x be the length of the sides perpendicular to the barn and let L be the total length of fence needed. Write the objective function. Lequals nothing (Type an expression.) The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be nothing m long and each of the sides parallel to the barn should be nothing m long. (Type exact answers, using radicals as needed.) Enter your answer in each of the answer boxes.