# Domain for this optimization problem

• Apr 5th 2011, 07:07 PM
IanCarney
Domain for this optimization problem
A farmer puts fencing around a rectangular field. He then uses more fencing to subdivide the field into three smaller "pens," such that each of the three pens are $\displaystyle 900 m^2$. He does this using the least amount of fence possible. What are the dimensions of the field.

$\displaystyle \displaystyle A=xy$

$\displaystyle \displaystyle 900=xy$

$\displaystyle \displaystyle y=\frac{900}{x}$

To find the domain, I would have thought that you needed to set each variable to be greater than or equal to zero, doing that would mean that $\displaystyle x$ can be any number greater than zero. Is that the correct domain?

Edit: And in the context of this problem, that would mean the only values I would test are where the slope equals zero to find the maximum/minimums?
• Apr 5th 2011, 07:20 PM
TheEmptySet
Quote:

Originally Posted by IanCarney
A farmer puts fencing around a rectangular field. He then uses more fencing to subdivide the field into three smaller "pens," such that each of the three pens are $\displaystyle 900 m^2$. He does this using the least amount of fence possible. What are the dimensions of the field.

$\displaystyle \displaystyle A=xy$

$\displaystyle \displaystyle 900=xy$

$\displaystyle \displaystyle y=\frac{900}{x}$

To find the domain, I would have thought that you needed to set each variable to be greater than or equal to zero, doing that would mean that $\displaystyle x$ can be any number greater than zero. Is that the correct domain?

Edit: And in the context of this problem, that would mean the only values I would test are where the slope equals zero to find the maximum/minimums?

You need one more constraint

Hint the the perimeter the amount of fence needed is

$\displaystyle P=2x+4y$ why?
• Apr 5th 2011, 07:27 PM
IanCarney
Quote:

Originally Posted by TheEmptySet
You need one more constraint

Hint the the perimeter the amount of fence needed is

$\displaystyle P=2x+4y$ why?

I understand the perimeter and have actually figured out the correct answer (as the minimum wasn't an end point) but I'm not sure what the other constraint is in terms of the domain.
• Apr 5th 2011, 07:32 PM
TheEmptySet
Quote:

Originally Posted by IanCarney
I understand the perimeter and have actually figured out the correct answer (as the minimum wasn't an end point) but I'm not sure what the other constraint is in terms of the domain.

Ahh I see you question the domain in terms of x is given by the open interval

$\displaystyle (0,\infty)$ so the domain does not have any end points to check.