# 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 