Question

A rectangular field, bounded on one side by a building, is to be fenced in on the other three sides. if 3000 feet of fence is to be used, find the dimensions

Answer 1

The question is missing the detail, it is to find the dimensions of the largest field that can be fenced in.
The formula for area is : A = xy
The perimeter of the fencing is equal to the sum of two widths and the length: 2x + y = 3000
Now, solve the second equation: y = 3000 – 2x
When you plug this expression to the formula for the area, we will get:
A = x (3000-2x) = 3000x – 2x^2
Next take the derivative and equal it to 0: dA/dx = 3000 – 4x = 0
Now solve for x, it will give us 750.
Find the second derivative.
d^2 A / dx^2 = -4
since we have a negative result, x = 75- is a maximum. Then plug this in to x:
3000 – 2 (750) = 1500. The largest field will measure 750 ft by 1500 ft.