07 Linear Programming

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Chapter 6 Supplement : 

Chapter 6 Supplement Linear Programming

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 Linear Programming

Linear Programming Model : 

Linear Programming Model Objective: the goal of an LP model is maximization or minimization 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

Linear Programming Assumptions : 

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

Graphical Linear Programming : 

Graphical Linear Programming 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

Linear Programming Example : 

Linear Programming Example

Linear Programming Example : 

Linear Programming Example

Linear Programming Example : 

Linear Programming Example

Slide 9: 

MS Excel worksheet for microcomputer problem

Slide 10: 

MS Excel worksheet solution

Constraints : 

Redundant constraint: a constraint that does not form a unique boundary of the feasible solution space Binding constraint: a constraint that forms the optimal corner point of the feasible solution space Constraints

Slack and Surplus : 

Slack and Surplus Surplus: when the optimal values of decision variables are substituted into a greater than or equal to constraint and the resulting value exceeds the right side value Slack: when the optimal values of decision variables are substituted into a less than or equal to constraint and the resulting value is less than the right side value

Simplex Method : 

Simplex Method Simplex: a linear-programming algorithm that can solve problems having more than two decision variables Tableau: One in a series of solutions in tabular form, each corresponding to a corner point of the feasible solution space

Sensitivity Analysis : 

Sensitivity Analysis Range of optimality: the range of values for which the solution quantities of the decision variables remains the same Range of feasibility: the range of values for the fight-hand side of a constraint over which the shadow price remains the same Shadow prices: negative values indicating how much a one-unit decrease in the original amount of a constraint would decrease the final value of the objective function

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