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Airplane luggage

Anonymous Wed 08 Jan 18:41:16 2020 No.11287115 View Reply Original Report

Quoted By: >>11287143 >>11287212 >>11287677 >>11289804

Some airlines cap checked bags at 62 linear inches, meaning the sum of width, height, and length. What dimensions would yield the highest volume?

x+y+z<=62
Max x*y*z+???

Anonymous

Anonymous Wed 08 Jan 2020 18:51:49 No.11287136 Report

Quoted By: >>11287688

>three variables
>two constraints
Uh oh.
x+y+z=62 means z=62-x-y
dV/dx= d/dx (xy(62-x-y)) = 62y-2xy-y^2; ddV/dxdy = 62-2x-2y
So 2x+2y=62 is your best bet unless that's a saddle point and I can't be fucked to continue

Anonymous

Anonymous Wed 08 Jan 2020 18:54:40 No.11287143 Report

Quoted By: >>11287688

>>11287115
All dimensions being 62/3 inches is maximum volume.

Finding a global maximum using math doesn't super work out because you get zeroes with partial derivatives. I just used Wolfram alpha to maximize within a domain.

This is kind of intuitive though since a cube is the closest you can get to a sphere, and your dimensions are kind of like perimeter/ surface area. Spheres maximize volume to surface area of any shape.

Anonymous

Anonymous Wed 08 Jan 2020 19:07:05 No.11287165 Report

Quoted By:

thanks guys. I'm flying frontier. Wish me luck

Anonymous

Anonymous Wed 08 Jan 2020 19:36:39 No.11287212 Report

Quoted By: >>11287688

>>11287115
F(x,y,z,l) = x*y*z - l(x+y+z-62)
Take the partial derivative of x,y,z gives
yz = l
xz = l
xy = l

we then get xy = yz <==> x = z
then do the same with xy = xz <==> y = z

and we get a maximum at x = y = z for the condition x+y+z-62 = 0 <==> 3x-62 = 0 <==> x=62/3

Anonymous

Anonymous Wed 08 Jan 2020 23:45:46 No.11287677 Report

Quoted By:

>>11287115
A cube

Anonymous

Anonymous Wed 08 Jan 2020 23:51:22 No.11287688 Report

Quoted By: >>11288212

>>11287136
>>11287143
>>11287212
I can't believe mathlets expend so much brain power trying to work out these problems in their heads. Just brute force it with a nested loop lmao.

Anonymous

Anonymous Thu 09 Jan 2020 05:20:22 No.11288212 Report

Quoted By:

>>11287688
writing a computer program takes more time than recognizing an obvious symmetry and exploiting it immediately

Anonymous

Anonymous Thu 09 Jan 2020 22:55:04 No.11289804 Report

Quoted By:

>>11287115
how will they measure a spherical bag? but if you're sticking with boxes it's easy to see that it's a cube.

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