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3.4 Optimization Continued
1. An open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size
from the corners and bending up the sides. What size square should be cut out to create a box with
greatest volume? What is the maximum volume as well?
2. Suppose you want to enclose a 5000 square foot yard. What is the least amount of fencing you can
use?
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Exercises:
Hint-Draw the picture first!
1. A manufacturer wants to design an open box having a square base and a surface area of 108 square
inches. What dimensions will produce a box with a maximum volume. What will this volume be?
2. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and the
square that produce a minimum total area. What is the total area?
3. Suppose you had 102 meter of fencing to make two side-by-side enclosures. What is the maximum
area you could enclose?
4. A silo is to hold 9,000 cubic feet of grain. The silo will be cylindrical in shape and have a flat top. Find
the dimensions of the silo that will use the least material for construction.
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