A rectangular animal pen will use 100 meters of fencing to enclose three sides

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A rectangular animal pen will use 100 meters of fencing to enclose three sides, while an existing barn forms the fourth side. If

x

meters is the length of each fence segment perpendicular to the barn and

y

meters is the length parallel to the barn so that

2x+y=100

, which dimensions maximize the area of the pen? (a)

x=25\text{ m},\;y=25\text{ m}

(b)

x=50\text{ m},\;y=25\text{ m}

(c)

x=25\text{ m},\;y=50\text{ m}

(d)

x=\dfrac{100}{3}\text{ m},\;y=\dfrac{100}{3}\text{ m}