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Optimization More Box Problems.doc Name_______________________________ 1) A cardboard box with square ends needs to be constructed to hold 8000 cubic inches of popcorn. Determine the dimensions that will minimize the amount of material needed to construct the box. x y x 2) An open box with square base is to be made from 192 ft.2 of material. What dimensions will result in a box with the largest possible volume? OPEN TOP 3) You are asked to construct a box whose length is 3 times its width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to build the box CLOSED TOP Height Width Length 4) A tank with a rectangular base and rectangular sides is open at the top. It needs to be constructed with a width of 4 meters and a volume of 36 cubic meters. The material costs $4 per square meter for the base and $2 per square meter for the sides. Determine the dimensions that will minimize the cost to build the box open y 4 x