Question

Using optimization find the length and width of a rectangle with maximum area that has a perimeter of (4P) units.

Answer 1

\(A(l,w) = lw\)
\(P(l,w) = 2l + 2w \quad [= 4\mathbf P]\)

\(\nabla A = \lambda \nabla P \\ \implies <w,l> = \lambda <2,2>\)

you want a square, i think.

Answer 2

Okay thank you!