SOLUTION: Hello, I need help with this problem. Thank you. The U.S. postal requires that any box sent by Priority Mail have length plus girth (distance around) totaling no more than 108 i

Question 967665: Hello, I need help with this problem. Thank you.
The U.S. postal requires that any box sent by Priority Mail have length plus girth (distance around) totaling no more than 108 in. The maximum volume that meets this condition is contained by a box with a square end 18 in. on each side. What is the length of the box? What is the maximum volume?
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the box has a square end of 18 inches on each side, then the girth of the box will be 4 * 18 = 72 inches.

the girth winds up being the perimeter of the end of the box.

that means the length has to be 108 - 72 = 36 inches.

the volume of the box will be 36 * 18^2 = 11,664 cubic inches.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The U.S. postal requires that any box sent by Priority Mail have length plus girth (distance around) totaling no more than 108 in.
The maximum volume that meets this condition is contained by a box with a square end 18 in. on each side. What is the length of the box? What is the maximum volume?
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Equation:
length + 4*18 = 108
length = 108-72 = 36 in
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Volume = (area of base)*height = 18^2*36 = 360 cu in
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Cheers,
Stan H.
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