# Chapter_2_Y2012_ - Chapter2 1 Introduction We all face...

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1 Introduction to Optimization  and Linear Programming Chapter 2
2 Introduction We all face decision about how to use limited resources such as: Oil in the earth Land for dumps Time Money Workers
3 Mathematical Programming... MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business, and is also referred to as optimization.
4 Applications of Optimization Determining Product Mix Manufacturing Routing and Logistics Financial Planning
5 Characteristics of  Optimization  Problems Decisions Constraints Objectives
6 General Form of an Optimization  Problem MAX (or MIN): f 0 (X 1 , X 2 , …, X n ) Subject to: f 1 (X 1 , X 2 , …, X n )<=b 1 : f k (X 1 , X 2 , …, X n )>=b k : f m (X 1 , X 2 , …, X n )=b m Note: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem
7 Linear Programming (LP) Problems MAX (or MIN): c 1 X 1 + c 2 X 2 + … + c n X n Subject to: a 11 X 1 + a 12 X 2 + … + a 1 n X n <= b 1 : a k 1 X 1 + a k 2 X 2 + … + a kn X n >=b k : a m 1 X 1 + a m 2 X 2 + … + a mn X n = b m
8 An Example: LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: tub A & tub B. There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.