a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? Bam b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? 25 25 25 25 a. Lot Abo 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 bar A (Type an expression.) The interval of interest of the 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 m long and the side parallel to the bar should be mlong. (Type exact answers, using radicals as needed.) b. Let X be the length of the sides perpendicular to the bar and let L be the total length of fence needed. Write the objective function. (Type an expression) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To minimize the amount of fore that it haar aarh the elde naman din for in the ham ehuldhaminnnandi aarhl the wires narallel to the home il Enter your answer in each of the answer boxes