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Find the double integral over the rectangular region R with the given boundaries. yext " dx dy; 3 sx= 4, 0 sys4 R I Svexty? dx dy= R (Type an exact answer in terms of e.)Find three positive numbers whose sum is 117 and whose product is a maximum. Let x be the first number, let y be the second number, and let z be the third number. Construct f(x,y,z) and g(x,y,z), the two functional parts of the Lagrange function, F(x,y,z,A) = f(x,y,z) - 2 . g(x,y,z). f( x, y,z) = g(x, y,z) = The relative maximum value is f (Simplify your answers.)Find the relative maximum value of f{x,y) = 4xy, subject to the constraint 2:: + 2y = 20. The relative maximum value is f( , = (Simplify your answers.) Find the volume under the given surface 2 =f(x, y) and above the rectangle with the given boundaries. z=6x+4y+7; 4sx54, 35y56 What is the volume of the region? B units3