Inch Rectangular
Inch Rectangular
A rectangular piece of cardboard on the face 24 by 36 inches is used to manufacture a box to open top by reducing SMA
A rectangular piece of cardboard on the face 24 by 36 inches is used to manufacture a box to open top by a small square cut each corner and fold the sides. For the box to receive a maximum volume, the edge of each of the cuts must be RESPONSE inches long.
The dimensions of The resulting picture is 24 x - 36 by 2x - 2x (helps to draw a picture). While the volume is 4x ^ 3 - 120x ^ 2 + 864x. The maximum occurs at a critical time we must root the V '= 12x ^ 2 - 240x + 864 = 0. Well, x ^ 2 - 20x + 72 = 0 has roots 10 + / - sqrt (28) ~ 15.29, 4.71. The solution required 15.29 subtract 30.58 24-inch, which is impossible, leaving 4.71 square inches on each side to maximize the volume. (You must verify that x = 4.71 is a local maximum in the test first or second derivative, but it is clear from the context it should be.)
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