Find the points on the ellipse x+2y2 = 1 where f(x,y) = xy has its extreme values. 13.10.3 Minimum surface area with fixed volume. Find the dimensions of the closed right circular cylindrical can of smallest surface area whose volume is 16 cm. 13.10.4 Rectangle of greatest area in an ellipse. Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse += 1 with sides parallel to the coordinate axes. 16 13.10.5 Extrema on a circle. Find the maximum and minimum values of x + y subject to the constraint x2-2x + y-4y = 0.