a rectangular box, open at the top, is to be constructed from a rectangular sheet of cardboard 80 centimeters by 50 centimeters by cutting out squares of equal size from the corners and folding up the sides. what side length do the cut-out squares need to have so that the resulting container has the maximum volume possible? draw a picture and label relevant variables! specify the domain of your objective function!

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15-11-2022
Mathematics

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a rectangular box, open at the top, is to be constructed from a rectangular sheet of cardboard 80 centimeters by 50 centimeters by cutting out squares of equal size from the corners and folding up the sides. what side length do the cut-out squares need to have so that the resulting container has the maximum volume possible? draw a picture and label relevant variables! specify the domain of your objective function!

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contexto1028 contexto1028 · Answer 1 · 2022-11-27T10:48:49-05:00

The volume first increases and then decreases as the length of the side of the square cut from each corner increases.

The volume of such a box is V= lxbxh V (80-2x)(50-2X) (X) Vat 4000x-260x2 + 4x3 = objective 50-2x 80-2XX function r(x) = 4000 (1) -260(27) + U(3x2) v(x)=4000-5207 + 1222 Vlx) = 4 [ 1000-1302 + 3x2) for the critical point V'ou = 0

50-2x=50-2(1) = -50 3. This is a negative number, but the width cannot be negative.

V"(x) = 0-520(1) +12 (2x) = 24x-520

Henu

V" (10) = 24(10)- 520 = - 280 Co X=10cm will augment volume.

V = (80-20), (50-20), (10) = 60x30x10 V = 18000 cubic centimeters is the maximum volume.

domain 50-270 twice 50 2250 times 25 domain jE

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