Asked by Alan
The US Post Office has a limit on the size of packages it will accept for mailing. The length plus the girth must be 84 inches or less. Find the dimensions of the rectangular package with a square end, which will maximize the volume of the package.
Answers
Answered by
Damon
4x +y = 84
so
y = (84-4x)
Volume = x^2 y = x^2(84-4x)
V = 84 x^2 - 4 x^3
dV/dx = 0 for max or min
0 = 168 x - 12 x^2
0 = x (168-12 x)
x = 0 not very useful so
x = 168/12 = 14
y = length = 28
interesting, length twice the side dimension
so
y = (84-4x)
Volume = x^2 y = x^2(84-4x)
V = 84 x^2 - 4 x^3
dV/dx = 0 for max or min
0 = 168 x - 12 x^2
0 = x (168-12 x)
x = 0 not very useful so
x = 168/12 = 14
y = length = 28
interesting, length twice the side dimension
Answered by
Alan
Wait don't you plus x=14 back in to y=(84-4x)? Cause y then equals 20 in
Answered by
Damon
well on my calculator 84 -14*4) = 28
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.