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3. Rectangular boxes with a volume of 8 ft' are to be made of three materials. The material for the bottom of the box costs $12 per ft?, the top of the box costs $4 per ft2 and the material for the sides costs $10 per ft2. What are the dimensions of the box that minimizes the cost of the box? Show all work. Round final dimensions of the box to the nearest tenth of a foot. (1 decimal place) 4 pts 4. Use the method of Lagrange Multipliers to find the maximum and minimum values of f(x, y) =xy2 subject to the constraint x2 + y =8. Show all work. 4 pts