Question

A fence must be built to enclose a rectangular area of ft. Fencing material costs per foot for the two sides facing north and south and ​$ per foot for the other two sides. Find the cost of the least expensive fence.

Answer 1

The complete question is

A fence must be built to enclose a rectangular area of 5000ft^2. Fencing material costs $1 per foot for the two sides facing north and south and 2$ per foot for the other two sides. Find the cost of the least expensive fence.

Answer:

Total cost will be $400

Step-by-step explanation:

Let x = be other side

     y =  north and  south side  

Area = x*y = 5000

Perimeter of the rectangle  = 2x + 2y

cost of fencing = 2(1)*5000/x + 2*2x

                         = 10000/x + 4x

 now to get the least we will take the derivative of this

C'(x) = 10000(-1/x^2)  + 4 =0

        x^2 = 2500

            x= 50ft cost = 2*$2*50 = $200

             y= 100ft  cost = 2*$1*100 = $200

Total cost = $400