A fence must be built to enclose a rectangular area of 5000 ft2. 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. The cost of the least expensive fence is .

The cost of the least expensive fence is $400

Step-by-step explanation:

Let the side of the area facing north and south = x

Let the side of the area facing west and east = y.

Perimeter, P(x,y)=2(x+y)=2x+2y

Fencing material costs $1 per foot for the two sides facing north and south and $2 per foot for the other two sides.

Therefore, Cost of Fencing=($1 X 2x)+($2 X 2y)=

C(x,y)=2x+4y

We can write the cost function as a function of one variable by substituting for y.

Recall: xy=5000

Therefore:

To determine the cost of the least expensive, we minimize C(x) by taking its derivative and solving for its critical points.

Therefore, the cost of the least expensive fence will be: