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 $21 per linear foot, and the material that will be used for the fourth side costs $15 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 $21 per linear foot.

Question

Braydon Phelps

Mathematics

24 April, 19:48

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 $21 per linear foot, and the material that will be used for the fourth side costs $15 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 $21 per linear foot.

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Parks · Answer 1

The problem is stated as:

Min C = 15 * (2*x + y) + 21*y

subject to x*y = 450

Step-by-step explanation:

Given that the region is rectangular, it has two opposite sides called x and two other opposite sides called y (both measured in feet). Then, the area (in square feet) is:

A = x*y = 450

One of the sides called y costs $21 per linear foot. The other 3 sides (two x and one y) costs $15 per linear foot. Then, the cost function is:

C = 15 * (2*x + y) + 21*y