# Optimization Problems by Z46iFdC6

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```									  Optimization Problems
To optimize a situation means to
find the “BEST” possible solution.
i.e. …maximize the volume
…minimize the cost
…maximize the area
…minimize the surface area
Optimization Problems

Constraint Equation:
Constraints are limitations or
restrictions associated with
constants given in the problem.
Optimization Problems

Objective Function:
The objective is to minimize or
maximize some quantity in the
problem.
Optimization Problems

Example 1:
Find the largest product possible
for two whole numbers whose
sum is 24.
Optimization Problems
Sum of whole numbers is 24   Largest product
possible
Fencing in a Garden
• A man wants to plant a rectangular
garden along one side of his house
with a fence on the other three sides
(to keep out the bunny rabbits).

• Find the dimensions of the largest
garden that can be enclosed using 40
feet of fencing.
Homework Questions #1 – 11
Homework Questions #1 – 11
U. S. Parcel Post
• U. S. Parcel Post regulations state that
packages must have length plus girth
of no more than 84 inches.

• Find the dimensions of the cylindrical
package of greatest volume that is
mailable by parcel post.
Golf Problem

• A net enclosure for practicing golf
is open at one end, which is square.
• The volume of the enclosure is to
be 83 1/3 cubic meters.
• Find the dimensions that require
the least amount of netting.
Swimming Club
• A swimming club offers memberships at the rate
of \$200, provided that minimum of 100 people
join.
• For each member in excess of 100, the
membership fee will be reduced by \$1 per
person (for every member.)
• At most 160 memberships will be sold.
• How many memberships should the club try to
sell in order to maximize revenue?

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