optimization prob.

G

Guest

Guest
Hi guys,

I think I am on track but am getting stuck.
Here is the problem:

A farmer wants to fence an area of 10000 square feet in a rectangular field and then divide it into 3 equal-size fields with fences parallel to one of the sides of the rectangle. What are the dimensions of the big field that will minimize the cost of the fence?

So here's what I have done:
Area expressed as a fcn of the variables: A = L*W, A = 3x+y,

So now,
6x+4y = 10000
3x+2y = 5000

So,
2y = 5000 - 3x
y = 2500 - 1.5x

A = 3x+y so
A(x) = 3x * (2500-1.5x)
= 7500x - 4.5x^2

We know for the domain x> 0 and 6x < 10000....

I think I now need to find critical numbers? So something like:

A(x) = 7500x - 4.5x^2
A'(x) = 7500 - 9x
9x = 7500
x = 833.33 is a crit point

So here is where I am stuck??? I imagine we have to evaluate the fcn at the critical number or something but I am not seeing it... Can you guys give me a hand. Thanks in advance.

Chris
 
What do the critical points of the "area" function give you?

Eliz.
 
could I plug the crit point into y = 2500 - 1.5x to give me the y? Im not sure im confused
 
Sorry, but you are in trouble from
A = 3x+y
You are adding two linear measures and claim the sum is an area. Bad units. What you probably wanted was
A = 3*x*y
Would you like to try it again with that correction or do you want little kids to point at you and laugh as you walk thru the fields?
 
Simple but fatal to the solution. Can you take it from there or...?
 
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