Optimization Problems by Z46iFdC6


									  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
  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
     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
• 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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