Suppose you need to minimize the cost of fencing a rectangular region with a total area of 550 square feet. The material for three sides costs $18 per linear foot, and the material for the fourth side costs $21 per linear foot.

Write a function that expresses the cost of fencing the region in terms of the length, [tex]x[/tex], of the two opposite sides of 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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