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a. A rectangular pen is built with one side against a barn. If 800 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an Barn area of 100 m (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? 100 100 100 100 a. To maximize the area of the pen, the sides perpendicular to the barn should be m long and the side parallel to the barn should be m long. (Type exact answers, using radicals as needed.) b. 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.)Suppose a student wishes to minimize the objective function on a closed interval, but finds that it has only a single local maximum. Where should the student look for the solution to the problem? Choose the correct answer below. O A. Determine the value where the objective function is equal to 0. O B. Determine the value of each endpoint for the objective function. O C. Determine the value where the second derivative of the objective function is equal to 0. O D. Determine the value where the first derivative of the objective function is equal to 0.What two positive real numbers whose product is 75 have the smallest possible sum? III The numbers are and (Type exact answers, using radicals as needed.)