Clearly and logically show all work. Name: 3. (20 points) Find the dimensions of the rectangle, with the maximum perimeter, that can be in- scribed, with sides parallel to the coordinate axes, in the ellipse 1. Use Lagrange multi- pliers. (a) Sketch a graph. b2 (b) Write the constraint function. (b) (c) Write the function we are maximizing, based on your graph above. (d) Write the vector equation. (c) (e) Find the dimensions of the rectangle with maximum perimeter.