1. Aim: How do we solve optimization problems? A rectangular enclosure is constructed using a barn wall as one side and 63 m of fencing for the other three sides. Find the dimensions of the pen that gives the greatest area. What do we want to maximize? What values of x make sense? x Area Domain: 0 < x < 31.5

3. Steps for Solving Optimization Problems: 1) Read the problem carefully. 2) Draw a sketch. Label using variables for unknown quantities. 3) Write a function, expressing the quantity to be maximized or minimized as a function of one variable. 4) Determine the domain of the independent variable (the values for which the problem makes sense). This determines xmin and xmax. 5) Determine the maximum and minumum values by using your graphing calculator. Draw a sketch of the function you used, label your answer on your sketch, and then write your answer in a sentence.