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