Question
Asked Dec 2, 2019
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A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 114 inches (see figure). Find the dimensions of the package of maximum
volume that can be sent. (Assume the cross section is square.)
X =
y =
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A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 114 inches (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.) X = y =

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Expert Answer

Step 1

The combined length and girth can be expressed as,

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114 %3D у + 4х y 114-4x

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Step 2

The volume of the rectangular box is given as,

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V = Lx Bx H = yxxxx Express y interms of x by using the expression from stepl V (114-4x)x2 V =114x-4x3

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Step 3

To maximize the volume, differentiate the Volume functio...

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d -(114x -4x3) dx dx - (A) dV =114-12x dx dV Set = 0 114-12x2 = 0 114 12 x 3.08

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Tagged in
MathCalculus

Derivative