# Let's say I have $480 to fence in a rectangular garden. The fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $15 per foot. How can I find the dimensions of the largest possible garden.?

##### 1 Answer

Jan 31, 2015

Let's call the length of the N and S sides

Then the cost of the fence will be:

Then the **equation** for the total cost of the fence will be:

We separate out the

**Area:**

To find the maximum, we have to differentiate this function, and then set the derivative to

Which solves for

Substituting in the earlier equation

**Answer:**

N and S sides are 12 feet

E and W sides are 8 feet

Area is 96 square feet