Page 20 - How To Solve Word Problems In Calculus

EXAMPLE 5
A farmer has 1500 feet of fencing in his barn. He wishes to
enclose a rectangular pen, subdivided into two regions by a
section of fence down the middle, parallel to one side of the
rectangle. Express the area enclosed by the pen as a function
of its width x. What is the domain of the function?

Solution
Step1
We draw a simple diagram, labeling the dimensions of
the rectangle.

y

x x x

y

Step2
We express the area of the rectangle in terms of the vari-
ables x and y. Observe that the area of the pen is determined
by its outer dimensions only; the inner section has no affect
on the area.

A = xy

Step3
We use the constraint of 1500 feet of fence to obtain a
relationship between x and y.

3x + 2y = 1500

Next we solve for y in terms of x.

2y = 1500 − 3x

3
y = 750 − x
2

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