To start you off, how do we work out the area A and perimeter P of a rectangle?
The Lagrange multiplier technique spits these into a function A - l (P-20), where l is the multiplier, and asks us to differentiate this with respect to x,y and also l.
It should look like:
A = xy
P = 2(x+y) = 20
A- l (P-20) = xy - 2l (x+y-10)
Hopefully you know how to differentiate this with respect to x and y etc.
Hi. Were our answers helpful on your previous question last week as you never responded then. Yse Jim's method here and this is straightforward. you don't need to know what a lagrange multiplier is _ I have forgotten but can still solve this.
I assumed above that the answer has to be a rectangle (which can include a square). If any shape is allowed then the answer is a circle so your answer will have reciprocal of pi in it
Without using Lagrange multiplier method I'd have simply done it this way:
Let width=x and length =y
Area (A) = xy
Perimeter = 2y +2x= 20, so y+x =10 so y= 10-x
So A = x(10-x)= 10x-x²
To find the min/max: dA/dx= 10-2x which is 0 at the max/min , i.e. when x=5
Second derivative is negative (-2) so it's a maximum