SOLUTION: Suppose an airline policy states that all baggage must be  boxshaped with a sum of  length, width, and height not exceeding 168in. What are the dimension

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Question 1156758: Suppose an airline policy states that all baggage must be  boxshaped with a sum of  length, width, and height not exceeding 168in. What are the dimensions and 
volume of a  square­based box with the greatest volume under these  conditions?
Write a function for the volume V of the box in terms of  w, one of the edges of
 the square bottom. 
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Suppose an airline policy states that all baggage must be boxshaped with a sum of length, width, and height not exceeding 168in.
What are the dimensions and
volume of a square­based box with the greatest volume under these conditions?
Greatest volume would be a cube
= 56 by 56 by 56 which is 56^3 = 175,616 cu inches
:
Write a function for the volume V of the box in terms of w, one of the edges of
the square bottom.
w = one side of the square bottom
sum of the length, width and height = 168, the bottom is square, therefore:
h = (168-2w)
V = w^2 * h
replace h with (168-2w)
V = w^2 * (168-2w)
V = -2w^3 + 168w^2

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