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Management (MGO)
Vinh Quan

Chapter 2 An Introduction to Linear Programming  constraints  an equation or inequality that rules out certain combinations of decision variables as feasible solutions 2.1 A Simple Maximization Problem Problem Formulation  problem formulation (modeling)  the process of translating the verbal statement of a problem into a mathematical statement called the mathematical model  even though every problem has some unique features, most problems also have common features  decision variable  a controllable input for a linear programming model  non-negativity constraints  a set of constraints that requires all variables to be non-negative  mathematical model  a representation of a problem where the objective and all constraint conditions are described by mathematical expressions  linear programming model (linear program)  a mathematical model with a linear objective function, a set of linear constraints, and non-negative variables st  linear functions  mathematical expressions in which variables appear in separate terms and are raised to the 1 power 2.2 Graphical Solution Procedure  feasible solution  a solution that satisfies all the constraints  feasible region  the set of all feasible solutions Summary of the Graphical Solution Procedure for Maximization Problems  the steps of the graphical solution procedure for a maximization problem are summarized here: 1. prepare a graph of the feasible solutions for each of the constraints 2. determine the feasible region by identifying the solutions that satisfy all the constraints simultaneously 3. draw an objective function line showing the values of the decision variables that yield a specified value of the objective function 4. move parallel objective function lines toward larger objective function values until further movement would take the line completely outside the feasible region 5. any feasible solution on the objective function line with the largest value is an optimal solution Slack Variables  slack variable  a variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality; the value of this variable can usually be interpreted as the amount of unused resource  standard form  a linea
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