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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