A box is?to be built entirely with cardboard with an open top, and is divided into three internal partitions of equal dimensions (left, right, and center) so that each partition has a square bottom. The bottom of the box will be made from cardboard that costs 5 cents per square foot, while the side (including front and back) are made from cardboard costing 4 cents per square foot. The cardboard forming the internal dividers will cost 2 cents per square foot. If the cardboard budget is 80 cents (including cardboard used as dividers), what should the dimensions (width, heigth, front-to-back depth) of the box be to maximize total volume, and what is that maximum total volume? Please include a labeled illustration of the problem so I can better follow the problem. Thank you!
5 cents for the bottom ? (5)(3x)(x) = 15x2 4 cents for the 4 sides ?
(2)(4) (3x)(y) + (x)(y) = 32xy 2 cents for the 2 dividers All together: Volume: ? (2)(2)(x)(y) = 4xy g(x, y) = 15x2 +...
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