Fence Question - Calculus

Question

A farmer wants to fence off a rectangular area of his property for his alpacas. In order to give the alpacas enough space he needs an area of 2700 square metres. One side of the area has to run along a road the remaining three slides are on his property. The cost for building a fancy fence along the road is $10 per metre, whereas the cost for building a much simpler fence along the remaining three sides that are on his property is only $6 per metre. The farmer wants to minimise the costs for fencing this area. What are the measurements of the rectangle for which the costs are minimised and what are the minimum costs?

I can't seem to set up this question in a way that makes sense to me.

My thinking right now is to set up an equation by doing something like:

2700 = 6x * (6y+10y)

Answer 1

Draw and label a diagram

w represents the width of the fence (perpendicular to road)

2700 / w represents the length of the fence (parallel to road)

C(w) = 10(2700 / w) + 6(2w + (2700 / w))

Can you simplify and determine minimum (use first derivative).