Question

A farmer is planning a rectangular area for her chickens. the area of the rectangle will be 450 square feet. three sides of the rectangle will be formed by fencing, which costs $5 per foot. the fourth side of the rectangle will be formed by a portion of the barn wall, which requires no fencing. in order to minimize the cost of the fencing, how long should the fourth side be?

Answer 1

Let x represent the length in feet of the area along the barn wall. Then the width of the area (out from the wall) will be 450/x, and the total cost of fence will be
cost = 5*(x +2*450/x)

A graphing calculator shows the minimum of the cost function is where x=30.

In order to minimize the cost of fencing, the fourth side should be 30 ft long.