# maximum and minimum

• May 1st 2011, 06:15 AM
Rine198
maximum and minimum
A wire of length 100cm is cut into two pieces of length xcm and ycm. The piece of length xcm is bent into the shape of a square and the piece of length ycm into the shape of a circle. Find x and y so that the sum of the areas encloseed by the shapes will be (a) a minimum (b) a maximum

I gathered that one of the equation will be x+y=100 but im not sure what the other equation will be, please help me with this? thanks
• May 1st 2011, 06:31 AM
SpringFan25
http://quicklatex.com/cache3/ql_4fcc...c9f5f7a_l3.png

solve using whatever method you have been taught
• May 1st 2011, 06:48 AM
Rine198
i don't get why the area of a circle is y/4Pi?
• May 1st 2011, 11:34 AM
SpringFan25
oopsie i did it wrong

circumference = y = 2pi r

rearrange so you have the area (pi * r * r) on one side.

http://quicklatex.com/cache3/ql_6bb2...d206afa_l3.png

the RHS is the area of the circle
• May 2nd 2011, 01:10 AM
Rine198
so i subbed in the equations and then differentiate it to get the st. pts. and got

x=400/(Pii+4)

and

y=100Pi/(Pi+4)

but i test the nature for this and wasn't able to prove it to be a minimum or a maximum point. why is that?
• May 2nd 2011, 03:17 AM
SpringFan25
show your calculations, it looks like a minimum to me: