Question

optimization:
Find the dimensions of a rectangle with area 1000m^2 whose perimeter is as small as possible.

Answer 1

square is the smallest perimeter rectangle... i think

Answer 2

1. Draw a picture of the rectangle.
2. Label its width (w) and its length (l).
3. Write a formula for the AREA of this rectangle, in terms of w and l.
4. Write a formula for the PERIMETER of this rectangle, also in terms of w and l.
5. Eliminate either w or l by substitution, in the formula you found in (4), above.
6. Find the derivative of the PERIMETER function.
7. And so on. Let me know if you need further guidance with this.

Answer 3

I am blanking on the best way to eliminate w or l?

Answer 4

What is the area of the rectangle?
The area of a rectangle, as you know, is (length)*(width).
You can solve the resulting equation for either w or l. Your choice.

Answer 5

So I got that p=2(A/L) + 2L, but how do I take the derivative? When I take the derivative of W, A, and L, do I write them as dW/dx, etc?

Answer 6

P=2(A/L) + 2L is fine. Rewrite that as\[P=2[AL ^{-1}+L]\]Recall that A is a constant whose value is known; L is the independent variable and P is the dependent variable.