1) Maximize the function f(x, y) = 10xy subject to the constraint 9x2 + 2532 = 225 Hint: Use Lagrange multipliers, take the two equations Fr = 0 and Fy = 0, isolate 2 in each one, and set these two equations equal to each other to give a relation between x and y.2) A closed rectangular box with a square base must have a volume of 8 cubic feet. The material for the top and sides is 50 cents per square foot, and the material for the bottom is 80 cents per square foot. Find the dimensions that minimize cost