Answer :
The function that expresses the cost of fencing the region: Cost(x) = 36x + 39y
How to find the region with material costs of $18 per linear foot.
Let's assume the length of the two opposite sides of the rectangular region with material costs of $18 per linear foot is x, and the length of the other two sides (including the side with material costs of $21 per linear foot) is y.
The total cost can be calculated as follows:
Cost = Cost of three sides with $18 per linear foot + Cost of the fourth side with $21 per linear foot
Since the perimeter is equal to 2 times the sum of the lengths of the two opposite sides (x), we have:
Cost of three sides = 2 * (x + y) * $18
The cost of the fourth side with $21 per linear foot is equal to the length of that side (y) multiplied by the cost per linear foot:
Cost of the fourth side = y * $21
we can express the total cost of fencing the region in terms of the length x of the two opposite sides:
Cost = 2 * (x + y) * $18 + y * $21
Simplifying this expression, we get the function that expresses the cost of fencing the region:
Cost(x) = 36x + 39y
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