Optimization problems with an open-top box — Krista King Math | Online math help
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Differentiation: Maximum Volume (examples, solutions, worksheets, videos, activities)
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A rectangular box with length x, width y, and height z is being built. The box is positioned so that one corner is stationed at the origin and the box lies in the first octant where x, y, and z are all positive. There is an added constraint on how the box is constructed: it must fit underneath the plane with equation x 2 y 3 z=6. In fact, we will assume that the corner of the box "opposite" the origin must actually lie on this plane. The basic problem is to find the maximum volume of the box. a.
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The length, width, and height of a rectangular box, in centimeters, ar
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Find the dimensions of the box with square base with: (a) Volume 12 and the minimal surface area. (b) Surface area 20 and maximal volume. | Numerade
Find the dimensions of the box with square base with: (a) Volume 12 a…
Apr 21, 2020
numerade.com
SOLVED:(a) A box is to be constructed out of 96 square feet of material. Find the dimensions x, y and z that maximize the volume of the box. (b) If the bottom of the box must be reinforced by doubling up the material (essentially, there are two bottoms of the box), find the dimensions that maximize the volume of the box.
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