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Suppose you need to minimize the cost of fencing in a rectangular region with a total area of 450 square feet. The material that will be used for three sides costs $15 per linear foot, and the material that will be used for the fourth side costs $18 per linear foot.

Write a function that expresses the cost of fencing the region in terms of the length, \( x \), of the two opposite sides of the region with material costs of $15 per linear foot.

Answer :

Answer:

30*x + 14850/x

Step-by-step explanation:

Let x be the length of the two opposite sides of the region with material costs of $15 per linear foot.

Let y be the length of the other two sides

Now, we have the following equations

Area of the rectangular región = x * y = 450 ft2

Total cost of fencing = 15*x + 15*x + 15 *y + 18*y

Total cost of fencing = 30*x + 33 *y

We now that area is equal to 450 ft2 = x*y

So y = 450/x

Now we can substitute y in equation for Total cost of fencing and obtain a function that expresses the cost of fencing the region in terms of the length, x

Total cost of fencing = 30*x + 33 *(450/x)

Total cost of fencing = 30*x + 14850/x

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