Can anyone please tell me how I need to go about solving this problem?

Question

Ok I am not looking for the answer I am just trying to figure out how to set up this problem so that I can find the answer so if you can please help I would greatly appreciate it!.......here is the problem.....a farmer wants to create a play space for his pet goats by enclosing a rectangle of land with a fence and then dividing it down the middle with another type of fence. the outer perimeter fence will cost $10 per foot and the fence across the rectangle (that divides the area into two parts) costs $5 per foot. find the dimensions of the rectangle that ives the largest amount of play space for $2006 worth of fencing, determine how much play space the farmer will have created

Answer 1

First draw a picture.
You will need to set up two equations: one relating $2006 to your two given costs and two variables indicating how much of each type of fencing.
Then you will need to set up another equation for the Area of the fence. The trick here is to relate the circumference to the dividing fence.
Once you have your two equations you will use Algebra to solve.

Answer 2

Suppose the rectangle has length L and width W. The perimeter is 2L + 2W, and that length of fence costs $10/ft, and there is the middle fence at $5/ft times W. This tells us that
(1) 10(2L + 2W) + 5W = 2006.

The area that you wish to maximize is given be A = LW. Use (1) to eliminate one of L or W from the area formula. Then you have area as a function of one variable, and proceed as usual to find a maximum.