a. A rectangular pen is built with one Slde against a barn lf 800 m of fencing are used for the other three SldeS ofthe pen. what dimensions maXImize the area ofthe pen? b. A rancher plans to make four Identical and adjacent rectangular pens against a barn. each With an area of 100 rn2 (see figure) What are the dimenSIons of each pen that minimize the amount of fence that must be used? a. LetA be the area ofthe rectangular pen and let x be the length ofthe sides perpendicular to the barn Write the objective function in a form that does not include the length ofthe side parallel to the barn. A: (Type an expressiion.) The interval ofinterest ofthe objective function is . (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 rn long and the side parallel to the barn should be m long (Type exact answers: using radicals as needed ) b. Let x be the length ofthe sides perpendicular to the barn and let L be the total length of fence needed Write the objective function. L : (Type an expresSion.) The interval ofinterest ofthe objective function is . (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints) To minimize the amount offence that must be used. each ofthe sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be m long. (Type exact answers. using radicals as needed )