Asked by matthew
A rectangular box with a volume of 64 ftcubed is to be constructed with a square base and top. The cost per square foot for the bottom is 15cents, for the top is 10cents, and for the sides is 2.5cents. What dimensions will minimize the cost?
Answers
Answered by
oobleck
If the base has side x, and the height is y, then
x^2 y = 64
The cost is
c(x,y) = 15x^2 + 10x^2 + 2.5 * 4xy
But, y = 64/x^2, so
c(x) = 25x^2 + 640/x
Now just find where c'(x) = 0
x^2 y = 64
The cost is
c(x,y) = 15x^2 + 10x^2 + 2.5 * 4xy
But, y = 64/x^2, so
c(x) = 25x^2 + 640/x
Now just find where c'(x) = 0
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.