# Use of differentiation in order to find the minimium value

1. Jul 9, 2006

The owner of a garden centre wishes to fence a rectangular area of 300 meters squared. She wished to fence three sides with a fencing that costs $9 per meter and the forth side with fencing costing$15 per meter. Find the dimensions of the rectangular area that will minimise her fencing cost.

I have started off this problem by drawing out a rectangle which I have labelled 2 sides as x and the other 2 as y. then I found y in terms of x according to the set area which was given. However I am not sure on how to proceed with this problem, as I am confused on how to find a function for the cost of this fencing. I know that this problem requires the use of differentiation in order to find the minimium value.

Thanks to anyone who helps and all input welcome ,

2. Jul 9, 2006

### StatusX

What are you confused about? The costs are found by multiplying the cost per meter by the length. Add up the costs of each side and minimize with respect to x (the area relation should allow you to eliminate y).

Last edited: Jul 9, 2006
3. Jul 10, 2006

### HallsofIvy

Staff Emeritus
Three sides of the fence are the less expensive $9 per foot material and one side is$15 per foot. You will need to decide whether it is an "x" or "y" side that has the more expensive material!

Suppose you choose "y" to represent the length with the $15 per foot material. How much would that cost altogether? Now you have 2 sides of length "x" and 1 side of length "y". How long is that altogether? How much will that cost at$9 per foot?

4. Jul 11, 2006