Question
Asked Nov 22, 2019
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Waste Management Company want to construct a
dumpster in the shape of a rectangular solid with no
top whose length is three times its width. Its
volume is fixed at 18 yds. Find the dimensions of
the dumpster that will minimize its surface area.
4.
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Waste Management Company want to construct a dumpster in the shape of a rectangular solid with no top whose length is three times its width. Its volume is fixed at 18 yds. Find the dimensions of the dumpster that will minimize its surface area. 4.

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Expert Answer

Step 1

Consider w as the width of the rectangular solid.

Then, the length is 3w.

Volume of the solid i...

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Volume wh 18 (3w)(w)h = 18 h= Зw? 6 h Surface area of the bottom (A1) = lw Surface area of sides, A 2wh+2(4wh) A2 10wh 6 A 10w 60 Total surface area, A 4 A 60 A = 3w dA = 6w dw 120

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Tagged in

Math

Calculus

Derivative