Please help! Some airlines have restrictions on the size of items of luggage tha
ID: 2848231 • Letter: P
Question
Please help!
Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 222 cm. A passenger wants to take a box of the maximum allowable volume. If the length and width are to be equal, what should the dimensions be?
length = width =
height =
In this case, what is the volume?
volume =
(for each, include units)
If the length is be twice the width, what should the dimensions be?
length =
width =
height =
In this case, what is the volume?
volume =
(for each, include units)
Explanation / Answer
vol = lwh
l+w+h=222
Case 1
l=w
h=222-2w
vol = w^2(222-2w) = 222w^2 - 2w^3
d(vol)/dw = 444w-6w^2
for a maximum
d(vol)/dw = 0
444w=6w^2
w = 444/6 = 74 cm
therefore l=w=h=74 cm (a cube)
do the same for
the next part using
l=2w
h=222-3w
vol=lwh = w x 2w x (222-3w) = 444w^2 - 6w^3
d(vol)/dw = 0
888w = 18w^2
w = 888/18 = 49.33
therefore l=2*49.33 = 98.66
h = 222-3*49.33 = 74.01