\fa. A rectangular pen is built with one side against a barn If 1600 rn of fencing are used forthe other three sides 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 400 m2 (see figure) What are the dimenSions of each pen that minimize the amount offence that must be used? a. LetA be the area ofthe rectangular pen and let x be the length otthe 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 expressmn.) The interval of interest 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 m long and the Slde 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 expressmn.) The interval of interest oftne 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 fence that must be used: each of the 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 ) A storage shed is to be built in the shape of a box With a square base. lt is to have a volume of 729 cubic feet. The concrete for the base costs $2 per square foot, the material for the roof costs $7 per square foot and the material for the sides costs $4 50 per square foot Find the dimensions of the most economical shed Let x represent the length of one otthe Sides ofthe base and let G represent the cost ofthe shed What is the objective function? C : (Type an expression) The interval of interest ofthe objective function is , (Simplify your answer. Type your answer in interval notation ) The length of one side ofthe sheo's base is ft The height otthe shed is ft