Problema Solution
A rectangular property has three sides fenced in against an existing river by 800 feet of wooden fencing. What are the dimensions of this field that maximize the amount of area used?
Answer provided by our tutors
Let 'x' and 'y' represent the sides of the rectangle and let 'y' be the side that is by the river (that doesn't need fencing).
2x + y = 800
y = 800 - 2x
The area is calculated by the formula:
A = x*y
plug y = 800 - 2x
A = x(800 - 2x)
A = -2x^2 + 800x
We need to fond the x such that A is maximum:
x = - b/2a, where a = -2, b = 800
x = - 800/(2*(-2))
x = 200 ft
y = 800 - 2*200
y = 400 ft
The dimensions of the field that maximize the amount of the area used are 200 ft and 400 ft.