AP4­2.1.notebook
December 01, 2011
OPTIMIZATION DAY 1
Procedure:
1. Draw diagram
2. Write a function in 2 variables to be minimized
or maximized.
3. Find a secondary equation to substitute into first equation. (constraint)
4. State the domain.
5. Use the first or 2nd derivative test to determine
max or min
1. A farmer needs to fence in a rect. plot of land
and then divide it equally using a section of
fence running parallel to two of the sides. What is the minimum length of fence needed
to enclose an area of 6,144 square feet?
2. A rect. box, open top, is to be made from
a 20 in. by 32 in piece of sheet metal by cutting identical squares from each of the corners and
folding the flaps. What is the length of the
sides of the squares that will maximize the
volume of the box?
1
AP4­2.1.notebook
December 01, 2011
3. A rectangle is topped by a semicircle whose
diameter is equal to the width of the rectangle.
If the perimeter of this shape is 200 inches, what is the maximum enclosed area?
4. A rectangle is inscribed in a semicircle. If
the radius of the semicircle is 3 meters, what
is the maximum area of the rectangle?
2