Thread: Cost of fence word problem

A rectangular area adjacent to a river is to be fenced in, but no fencing is required on the side by the river. The total area to be enclosed is 6000 square feet. Fencing for the side parallel to the river is $5 per linear foot, and fencing for the other two sides is $2 per linear foot. The four corner posts cost $30 apiece. Let be the length of the one the sides perpendicular to the river.


Find a cost equation

Find the minimum cost to build the enclosure:

well first find an equation for the lengths of the sides

A=(L)(w)
6000=(L)(x)
L=6000/x

so, the total amount of fence is going to be represented by the equation y=2x+6000/x

now fill in the prices to make it a cost function

C(x)=(2)(2x)+(5)(6000/x)+(4)(30)
C(x)=4x+30000/x+120

then you want to find the minimun you can do this by graphing the problem on a calculator and looking at it,or using the derivative to find the min.

C'(x)=4-(30000/(x^2))
0=4-(30000/(x^2))
30000/x^2=4
4(x^2)=30000
x^2=7500
x=sqrt(7500)

fill that value into the cost equation for x and solve an that will be the min cost