7. Suppose an architect is building a room whose oor is described by the rectangle R = [0,2] X [0, 4], and whose ceiling is described by the function f (1;, y) = m2 [all lengths measured in meters]. The architect needs to nd the average height of the ceiling. (8.] [1 Point} Show that f the average value of the function x, 1;] = my: on R is 16,33. {b} Find the point P where HP] 2 f that is closest to the center of the region. (Hint: Use Lagrange Multipliers minimize the distancesquared to the center of the room, and use the fact that f(z, y) = 15f3 as your constraint)