Question

American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight

Answer 1

The maximum volume is 35316.4 in^3.

Explanation:

Length + width + height is less than equal to 62 inches

Height = width = W

Let the length is L .

`L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)* W * W\\\\V = 62 W^2 - 2 W^3\\\\(dV)/(dW)=124 W - 6 W^2\\\\So, (dV)/(dW) =0\\\\124 = 6 W\\\\W = 20.67 inches`

So, the maximum volume is

`V =124* 20.67* 20.67 - 2 * 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3`