Name: 5. (20 points) Use Lagrange multipliers to find the dimensions of the rectangle with the maximum perimeter that can be inscribed with sides parallel to the coordinate axes in the ellipse -, + 1. (a) Sketch a graph. (b) Write the constraint function. (b) (c) Write the function we are maximizing, based on your graph above. (c) (d) Write the vector equation. (e) Find the dimensions of the rectangle with maximum perimeter