Chapter 2: Intro to Optimization and Linear Programming

general form of an optimization problem

MAX (or MIN); subject to:

mathematical programming (optimization)

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

special conditions in LP models

a number of anomalies can occur in LP problems: -alternate optimal solutions -redundant constraints (does nothing) -unbounded solutions (no solution, depending on side) -infeasibility (no overlap)

characteristics of optimization problems

decisions, constraints, objectives

applications of optimization

-Determining Product Mix -Manufacturing -Routing and Logistics -Financial Planning

solving LP problems: a graphical approach

-the constraints of an LP problem defines its feasible regions -the best point in the feasible region is the optimal solution to the problem -for LP problems with 2 variables, it is easy to plot the feasible region and find the optimal solution

5 Steps in Formulating LP Models

1. Understand the problem. 2. Identify the decision variables. 3. State the objective function as a linear combination of the decision variables. 4. State the constraints as linear combinations of the decision variables. 5. Identify any upper or lower bounds on the decision variables.

summary of graphing solution to LP problems

1. plot the boundary line of each constraint 2. identify the feasible region 3. locate the optimal solution by either: -plotting level curves -enumerating the extreme points