Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in. find the dimensions of a rectangular package that has a square cross section and largest volume that may be sent by priority mail. what is the volume in such a package?

The volume in such a package is 27648 in³

Step-by-step explanation:

Consider the provided information.

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in.

Let the dimension are x by x by y.

Where x is the variable for the square base package and y is the variable for length.

Thus l=x, b=x and h=y

Then the volume of the box is: (∵V=lbh)

The maximum combined length and girth is 144.

Therefore,

Substitute the value of y in volume of the box.

Substitute V'(x)=0.

Now apply second derivative test.

(Min)

(Max)

Hence, the maximum volume is at x=24

If x=24 then

Substituting value of x = 24 and y = 48 gives 27648.

Hence, the volume in such a package is 27648 in³

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step-by-step explanation: