A fence must be built to enclose a rectangular area of 45 comma 000 ftsquared. Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides. Find the cost of the least expensive fence.

150 feet by 300 feet.

Step-by-step explanation:

The fence is to enclose a rectangular area of 45,000 ft squared.

If the dimensions of the rectangle are x and y

Area of a rectangle = xy

Perimeter of the Rectangle =2x+2y

Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.

Substitute into the Cost to get C(y)

C=12x+6y

The value at which the cost is least expensive is at the minimum point of C(y), when the derivative is zero.

Recall,

Since x=150, y=300

The dimensions that will be least expensive to build is 150 feet by 300 feet.