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Answer:
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
- xy=45000
Perimeter of the Rectangle =2x+2y
Fencing material costs $ 3 per foot for the two sides facing north and south and $6 per foot for the other two sides.
- Cost of Fencing, C=$(6*2x+3*2y)=$(12x+6y)
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.