# Math Help - maximize

1. ## maximize

I can't even explain how lost i am on this problem so here it is.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.

2. Originally Posted by uniquereason81
I can't even explain how lost i am on this problem so here it is.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.
$P=2\pi{r}+2x$

Solve for x and sub into your A equation

Edit^(didnt read it again)

3. Originally Posted by uniquereason81
I can't even explain how lost i am on this problem so here it is.

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200-meter running track, find the dimensions that will make the are of the rectangular region as large as possible.
You want to maximize the area of a rectangular region, represented by $xy$, with the constraint of a 200 meter perimeter. The perimeter is going to be equal to the circumference of a circle (with diameter x) plus two sides (of length y) of the rectangle:
$\pi{x}+2y$

So given that $\pi{x}+2y=200$ maximize $xy$. Then I would assume you would use Lagrange multipliers.

4. Originally Posted by icemanfan
You want to maximize the area of a rectangular region, represented by $xy$, with the constraint of a 200 meter perimeter. The perimeter is going to be equal to the circumference of a circle (with diameter x) plus two sides (of length y) of the rectangle:
$\pi{x}+2y$

So given that $\pi{x}+2y=200$ maximize $xy$. Then I would assume you would use Lagrange multipliers.
.......Lagrange multipliers? Why would you ever do that..solve the P equation in terms of the other variable...substitute it into your A equation...differentiate and proceed to find max by normal methods

5. Originally Posted by Mathstud28
.......Lagrange multipliers? Why would you ever do that..solve the P equation in terms of the other variable...substitute it into your A equation...differentiate and proceed to find max by normal methods
You're right, this problem isn't too complicated to require doing it that way.

6. Originally Posted by icemanfan
You're right, this problem isn't too complicated to require doing it that way.
Haha you just tried to apply a Calc 3 method to a Calc 1 problem