Page 90 - How To Solve Word Problems In Calculus

EXAMPLE 2
Jodi wishes to use 100 feet of fencing to enclose a rectan-
gular garden. Determine the maximum possible area of her
garden.

Step1

y

x

Step2

A = xy

Step3
Since the perimeter of the rectangle is to be 100 feet,

2x + 2y = 100

x + y = 50

y = 50 − x

2
It follows from step 2 that A(x) = x(50 − x)or A(x) = 50x − x .
Since x cannot be negative, the smallest allowable value of x
is 0. Since y = 50 − x and y cannot be negative, the largest
allowable value of x is 50.

0 ≤ x ≤ 50

Note: In order to obtain a closed interval, we allow x = 0 and
x = 50 as acceptable dimensions. Such degenerate rect-
angles have an area of 0.

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