Asked by kk
A farmer has 25 yards of fencing to make a pig pen. He is going to use the side of the barn as one of the sides of the fence, so he only needs to fence 3 sides. What should be the dimensions of the fence in order to maximize the area?
Answers
Answered by
Reiny
let the side parallel to the barn be y yards
then the other two sides are x yards each
2x + y = 25
y = 25-2x
area = xy
= x(25-2x)
= 25x - 2x^2
which graphs as a downwards parabola, so the vertex has to be found.
quickest way:
the x of the vertex is -b/(2a) = -25/-4 = 6.25
then y = 25-12.5 = 12.5
the fields should be 12.5 long (along the barn) and 6.25 wide
then the other two sides are x yards each
2x + y = 25
y = 25-2x
area = xy
= x(25-2x)
= 25x - 2x^2
which graphs as a downwards parabola, so the vertex has to be found.
quickest way:
the x of the vertex is -b/(2a) = -25/-4 = 6.25
then y = 25-12.5 = 12.5
the fields should be 12.5 long (along the barn) and 6.25 wide
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.