Optimization Problems

1
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
2
Optimization Problems

• Constraint Equation
• Constraints are limitations or restrictions
  associated with constants given in the problem.

3
Optimization Problems

• Objective Function
• The objective is to minimize or maximize some
  quantity in the problem.

4
Optimization Problems

• Example 1
• Find the largest product possible for two whole
  numbers whose sum is 24.

5
Optimization Problems

• Sum of whole numbers is 24

Largest product possible
6
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.

7
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.

8
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.

9
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?