323
Answers
501–600
Answers and Explanations
Take the derivative and set it equal to zero to find x:
′
A
x
x
x
x
= −
= −
=
=
30 2
0 30 2
2
30
15 m
You can verify that this gives you a maximum by using the first derivative test.
Using 2x + 2y = 60 and x = 15 meters, you get y = 15 meters.
501.
56,250 ft
2
Let x and y be the lengths of the sides of the pen as in the following diagram:
From the diagram, you have the following perimeter formula:
5
2
1 500
x
y
+
= ,
The function you want to maximize, the area, is given by
A x y
xy
( , ) =
You can write this as a function of one variable by using the equation 5x + 2y = 1,500 to
get y
x
=
−
750 5
2
. Substituting the value of y into the area equation gives you
A x
x
x
x
x
( ) =
−
=
−
750 5
2
750
5
2
2
(
)
Take the derivative of this function, set it equal to zero, and solve for x:
′
A
x
x
x
x
=
−
=
−
=
=
750 5
0 750 5
5
750
150