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Use the region R with the indicated boundaries to evaluate the double integral. 3x y dydx; R bounded by y = x, y = 4x R Set up the double integral with appropriate bounds. 3x y dydx = 3x y dydx R 3x3y dydx = RThe Cobb-Douglas production function for a particular product is N(x,y) = 60x0'3y0'2, where x is the number of units of labor and y is the number of units of capital required to produce N{x, y} units of the product. Each unit of labor costs $60 and each unit of capital costs $120. If $600,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production. Production will be maximized when using D units of labor and D units of capital. Find three positive numbers whose sum is 102 and whose product is a maximum. Let x be he rst number, let y be the second number, and let 2 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,}t) =f(x.y,z) 9t- g(x,y,z). f(x,y,z)= XV?- g(x,y,z)= x+y+z 102 The relative maximum value isf 34 , 34 , 34 (Simplify your answers.)