Optimization Set-Up: Finding Optimal Dimensions for a Rectangle with Area 64m^2

[Hollysmoke]

We're doing optimization problems and I was just wondering if I set this one up right:

What are the dimensions of a rectangle with an area of 64m^2 and the smallest possible perimeter?

Area=xy
64=xy
y=64/x
Perimeter=2x+2y
= 2x+2(64/x)
= 2x+128/x

 

[PPonte]

Simple. In this case you have just to find the minimum value of the perimeter function for values of x > 0, then you find y and have the dimensions of the rectangle with the smallest perimeter.

Anyway, here is the plot of the functions. Pink - Perimeter; Blue - Area.

http://img296.imageshack.us/img296/3231/plot553br.png

 

[Hollysmoke]

We just started so we're not at THAT level yet, but thanks anyways D8