Question
Asked Oct 26, 2019
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An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a bin with the maximum volume?

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Expert Answer

Step 1

Assume that side of square which should be cut from each corner is a.

Given the dimension of piece of plastic is 15cm by 40 cm.

If the sides are cut from the corner in order to form an open bin, the dimension of the bin becomes,

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length 40 2a breadth 15- 2a height a

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Step 2

Compute the volume as follows.

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V(a) lbh -a(40-2a)(15-2a) = 4a3 -110a2 + 600a

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Step 3

Obtain the first and second derivative of  V ...

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V'(a) 12a-220a +600 V"(a) 24a 220

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