6S Linear Programming McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All Learning Objectives Describe the type of problem tha would lend itself to solution using linear programming Formulate a linear programming model from a description of a problem Solve linear programming problems using the graphical method Interpret computer solutions of linear programming problems Do sensitivity analysis on the solution of a linear progrmming problem 6S-2 Linear Programming Used to obtain optimal solutions to problems that involve restrictions or limitations, such as: Materials Budgets Labor Machine time 6S-3 Linear Programming Linear programming (LP) techniques consist of a sequence of steps that will lead to an optimal solution to problems, in cases where an optimum exists 6S-4 Linear Programming Model Objective Function: mathematical statement of profit or cost for a given solution Decision variables: amounts of either inputs or outputs Feasible solution space: the set of all feasible combinations of decision variables as defined by the constraints Constraints: limitations that restrict the available alternatives Parameters: numerical values 6S-5 Linear Programming Assumptions Linearity: the impact of decision variables is linear in constraints and objective function Divisibility: noninteger values of decision variables are acceptable Certainty: values of parameters are known and constant Nonnegativity: negative values of decision variables are unacceptable 6S-6 Graphical Linear Programming Graphical method for finding optimal solutions to two-variable problems Set up objective function and constraints in mathematical format Plot the constraints Identify the feasible solution space Plot the objective function Determine the optimum solution 6S-7 Linear Programming Example Objective - profit Maximize Z=60X1 + 50X2 Subject to Assembly 4X1 + 10X2