Hello, calc_help123!
A man has 340 yards of fencing for enclosing two separate fields,
one of which is to be a rectangle twice as long as it is wide and the other is a square.
The square field must contain at least 100 square yards
and the rectanglar one must contain at least 800 square yards.
a) If x is the width of the rectangular field, what are the maximum
and minimum possible values of x?
The rectangular field has width and length
The area of the rectangular field is: . yd˛.
Its perimeter is yards, leaving yards for the square field.
The side of the square field is: . yards.
The area of the square field is: . yd˛.
We are told that: .
. .
We are told that: .
. .
Therefore: .
b) What is the greatest number of square yards that can be enclosed
in the two fields? Explain.
The total area is: .
The graph is an upopening parabola.
Its vertex (lowest point) is: . Code:

 *

 *:
 * :
 * * :
 : * * :
 : * :
 : : :
 : : :
++++
 20 30 50

Hence, maximum area occurs at the endpoints of the interval.
Looking at the graph, we suspect it happens at ,
. . but we can verify this.
At
At . . . There!
The rectangle will be 50 × 100 yards.
The square has sides of 10 yards.