. Module 11 Assignment (, Josephine 6 ( ) Pre-Calculus B (Harris... Q D C?) Aceves Goal: Your goal is to use limits to maximize the area of a rectangular playground, given a certain amount of fencing. Role: You are in charge of building a rectangular play area for Lil' Tikes Preschool, where your little sister, who is 3, goes to school. Audience: The headmaster of LilI Tikes Preschool wants the play area to be the biggest size possible, because the kids like to run, but has limited you to only a certain amount of fencing, because of the budget, which has been cut significantly. Your audience is also the kids at the preschool, because they really do like to run, especially your sister. Situation: The context you find yourself in is that you have been given 24 meters of fencing material. You must maximize the rectangular area given this 24 meters of fencing. There are many rectangles that you can make using 24 meters of fencing, but only one that maximizes the area for the children. Product, Performance, and Purpose: Start with the equation for perimeter of this rectangle 2L + 2W = 24. Solve this equation for L, to get the Length in terms of W. Use this length in terms of W, to write an equation for the Area (remember, A=LW) in terms of W. This equation is your function, f(x)=your area equation. Graph this function in your graphing calculator and use the table to find the x-value(width) that corresponds to the maximum y-value(which is area). This is the width that will maximize the area. Show your table. To support your answer, use direct substitution to find the limit as x approaches this width of the function. This answer should match the y-value you found in the previous question. Finally, state the dimensions, length and width, of the rectangle with perimeter 24 meters that gives the rectangle a MAXIMUM AREA