Solutions to Quiz 8Awww.math.ufl.edu/˜harringtNovember 26, 20061.(3 pts.)Mrs. Zerta wants to start a garden next to her house. She only has 400yards of fencing. If fencing is NOT required along side of her house, what are thedimensions of the largest area that she can enclose? What is this area?Solution:We will letxdenote the width andydenote the length.So wehave this image:So we have that the perimeter isP= 2x+y= 400.Also recall that the areais:A=xy.Thus, we will solve foryusing the perimter.So,y= 400-2x.Next, we will substitutey= 400-2xback in the formula for area.Hence,A=x(400-2x) = 400x-2x2. This is the equation we want to maximize. Alsonote that,x≥0, andy= 400-2x≥0. So, 0≤x≤200. Therefore, we want
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