Question

A gardener wants to enclose a rectangular herb garden of area 600ft^2. To keep out critters, three sides require wire mesh fencing costing $30 per foot and the remaining side requires wooden boards costing $40 per foot. Find the dimensions that minimize the cost of the fencing.

Answer 1

we can do this

Answer 2

we need a function for the cost. here is a picture
total cost is \(30x+30x+30y+40y\) if we make \(y\) one of the sides that cost $40 per foot

Answer 3

better written as \(C=60x+70y\) now we have to relate \(x\) and \(y\) for that we use that the area \(A=xy\) is \(600\) so \(xy=600\) making \(y=\frac{600}{x}\)

Answer 4

that gives is
\[C(x)=60x+\frac{42000}{x}\] and you want the minimum cost ( for \(x>0\) )
take the derivative, set it equal to zero and solve

Answer 5

you good from there?