Question: Clearly and logically show all work. Name: 3. (20 points) Use Lagrange multipliers to find the dimensions of the rectangle with the maximum perimeter that

Clearly and logically show all work. Name: 3. (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 2 = 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. (e)

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