a. A rectangular pen is built with one side against a barn. lf 300 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 area of 225 m2 (see figure). What are the dimensions of Barn each pen that minimize the amount of fence that must be used? 225 225 225 225 E) a. To maximize the area of the pen, the sides perpendicular to the barn should be 75 m long and the side parallel to the barn should be 150 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.) A rectangular tank with a square base, an open top, and a volume of 6,912 ft3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The tank with the minimum surface area has a height of D ft and a square base with a side length of D ft. A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 9 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. E) a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? To minimize the total travel time, the boat should land miles from the restaurant. (Type an exact answer, using radicals as needed.) b. If she walks at 3 mi/hr, find the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)? The minimum speed she must row is mi/hr. (Type an exact answer, using radicals as needed.)