Question 5 Suppose that you want to create a rectangular animal enclosure using 80 linear feet of fencing. You also want to incorporate a pre-existing stone wall running 40 feet in a straight line. Stone Wall (40 ft) (a) Let x be the length of fencing used on the side containing the wall. Determine the side lengths for the remaining sides of the rectangle in terms of this x, keeping to the constraint that you have 80 feet of fencing available. (b) Determine the objective function A(x) for the area of the enclosure given the value of x. Determine the value of x that maximizes this function's output. (c) Based on the scenario, determine the appropriate restriction to the domain of A(x) and maximize area with respect to that restriction.

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