12.8 Key terms
Key Terms
- Constraints: Limitations or requirements (expressed as inequalities or equations) that the decision variables must satisfy, often related to resources like time or budget.
- Corner Points (Vertices): The intersection points of constraint lines in the feasible region. These are evaluated to find the optimal value in the graphical method.
- Decision Variables: Unknown quantities in an LPP whose values are to be determined (e.g., number of units to produce).
- Excel Solver: An optimization tool in Microsoft Excel that can solve LPPs using built-in algorithms like the Simplex LP method.
- Graphical Method: A visual technique for solving LPPs with two variables by plotting constraints on a graph and identifying the feasible region and optimal point.
- Linear Programming (LP): A mathematical technique used to optimize a specific objective (e.g., maximize profit or minimize cost) subject to a set of linear constraints.
- Linear Programming Problem (LPP): A mathematical model representing a real-world situation where the objective and constraints are linear. It includes an objective function, decision variables, and constraints.
- Non-negativity Constraints: A condition in LP that ensures all decision variables are equal to or greater than zero, reflecting real-world scenarios where negative values aren’t feasible.
- Objective Function: The formula that defines what needs to be optimized in an LPP—either maximized (e.g., profit) or minimized (e.g., cost).
- Simplex Method: An algebraic method used to solve LPPs with more than two variables. It systematically moves from one vertex to another to improve the objective value until optimality is reached.
- Slack Variables: Variables added to constraints to convert inequalities into equalities in the Simplex Method, representing unused resources.
- Standard Form (of an LPP): A canonical form where the objective is either maximized or minimized, all constraints are expressed as linear inequalities (≤), and variables are non-negative.
- Stepping Stone Method: An optimization technique used in transportation models that tests the potential of unused routes via closed loops to reduce costs.
- SUMPRODUCT Function: An Excel function used to compute dot products, useful for defining objective functions and constraint expressions in LP models.
