Sections 15.5 - Constrained Optimization: Lagrange Multipliers Preliminary Example. Let T = f(r,y) = ;(x' + y') be the temperature, in degrees Celsius, at a point (r, y) on a metal plate, where r and y are measured in cm. A contour plot for the function f T-3 is shown to the right. T=2 (a) Find the minimum temperature of the plate along the line r+ y =4 and the minimum temperature of the plate along the T-1 line r + y = -2. -3 -2 -1 T-4 (b) Let g(r, y) = r + y, and note that the lines r + y = 4 and r + y = -2 from part (a) are level curves of g. Draw the gradient vectors Vf and Vg at the two points from part (a) where the minimum temperature is achieved. (c) Examine the point on each of the two lines where the minimum temperature is achieved. How are the level curves of f and g related? How are the vectors Vf and Vg related