## anonymous 3 years ago optimization problem: a 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

1. anonymous

Do you know how to find the largest area possible?

2. anonymous

Draw a picture

3. anonymous

|dw:1353735822700:dw|

4. anonymous

lol

5. anonymous

That's fine lol

6. anonymous

c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up

7. anonymous

i think you have the perimeter wrong

8. anonymous

how?

9. anonymous

You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.

10. anonymous

You would need it to be $$2x + c = 200$$

11. anonymous

c is the circumference right

12. anonymous

Yes, and that's right ($$2 \pi r$$).

13. anonymous

okay and then differentiate that equation correct?

14. anonymous

You would need to differentiate the area, not the perimeter.

15. anonymous

So, can you first determine a formula for the area of your diagram?

16. anonymous

pir^2+2rx

17. anonymous

Yeah, that looks good.

18. anonymous

should i substitute r or x

19. anonymous

Whichever one you want

20. anonymous

100/3pi = r seem right?