LL . Of all rectangles with a perimeter of 21, which one has the maximum area? (Give the dimensions.) LetA be the area of the rectangle. What is the objective function in terms of the width of the rectangle, w? A = (Type an expression.) a. A rectangular pen is built with one side against a barn. If 1200 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 m (see figure). What are the dimensions of each pen Barn that minimize the amount of fence that must be used? 225 225 225 225 . . . a. Let A be 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 barn. A = | (Type an expression.)A rectangular tank with a square base, an open top, and a volume ot108 ft3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Lets be the length of one of the sides of the square base and letA be the surface area of the tank. Write the objective function. A = (Type an expression.)