Linear Programming

Graphical solution

________- becomes impractical when there are three or more variables involved in the problem.

Augmentation

________- The process of adding slack and /or artificial variables to constraints to generate equations.

Infeasibility

________- The condition when there is no solution which satisfies all the constraints in a problem.

Parameters

________- numerical coefficients and constants used in the objective function and constraint equations.

Inequality

________- A mathematical expression indicating that minimum or maximum requirements must be met.

simplex tableau

Pivoting - The process of going from one ________ to the next.

Constraints

________- is the linear mathematical expression of the relationships between the resource limitations and the resource requirements associated to the objective variables specified in a linear programming problem.

Redundancy

________- A constraint which does not affect the feasible region.

Extreme point

________- A corner of the feasible region.

Artificial variable

________- A computational device used in linear programming to achieve an initial solution to the problem.

Optimum column

________- That column in any solution to a maximizing problem which has the largest positive value in the Cj- Zj row or which has the largest negative value in a minimizing problem.

Simplex Method

________- is more appropriate method in solving complicated linear programming models.

Objective function

________- is the mathematical expression of the objective that the decision maker wants to achieve in a given linear programming decision situation, in terms of decision variables, that is to be maximized or minimized.

Cj Zj row

________- The row containing the net benefit or loss occasioned by bringing one unit of a variable into the solution of a linear programming problem.

Iterative process

________- A step- by- step process following a standard pattern.

Feasible region

________- The area containing all the possible solutions to the problem, which are feasible, that is, those solutions which satisfy all the constraint in the problem.

Market Constraints

________- These are limits on how many products can be sold or used.

Simplex method

________- is an iterative process.

Constraint

________- A limit on the availability of resources.

Produce products

such as computers, automobiles, or clothing or

Provide services

such as package delivery, health services, or investment decisions

Decision variables

mathematical symbols representing levels of activity of a firm

Objective function

is the mathematical expression of the objective that the decision maker wants to achieve in a given linear programming decision situation, in terms of decision variables, that is to be maximized or minimized

Constraints

is the linear mathematical expression of the relationships between the resource limitations and the resource requirements associated to the objective variables specified in a linear programming problem

Parameters

numerical coefficients and constants used in the objective function and constraint equations

Market Constraints

These are limits on how many products can be sold or used

Availability Constraints

These are limits because of scarcity of raw materials, funds or other resources

Quality or Blending Constraints

These are constraints that put limits on mixes of ingredient, usually defining the quality of output products

Material Balance Constraints

These are constraints that define the output of some process as function of the inputs, often with a loss for scrap

Constraint

A limit on the availability of resources

Extreme point

A corner of the feasible region

Feasible region

The area containing all the possible solutions to the problem, which are feasible, that is, those solutions which satisfy all the constraint in the problem

Inequality

A mathematical expression indicating that minimum or maximum requirements must be met

Infeasibility

The condition when there is no solution which satisfies all the constraints in a problem

Iso-cost line

A line representing all possible combinations of problem variables which produce the same total cost

Iso-profit line

A line representing all possible combinations of products which will produce a given profit

Non-negativity constraints

Constraints that restrict all variables to be zero or positive

Redundancy

A constraint which does not affect the feasible region

Structural Constraints

All constraints in a linear program besides the non-negativity constraints

Graphical solution

becomes impractical when there are three or more variables involved in the problem

Simplex Method

is more appropriate method in solving complicated linear programming models

Simplex method

is an iterative process

Artificial variable

A computational device used in linear programming to achieve an initial solution to the problem

Augmentation

The process of adding slack and/or artificial variables to constraints to generate equations

Cj-Zj row

The row containing the net benefit or loss occasioned by bringing one unit of a variable into the solution of a linear programming problem

Iterative process

A step-by-step process following a standard pattern

Optimum column

That column in any solution to a maximizing problem which has the largest positive value in the Cj-Zj row or which has the largest negative value in a minimizing problem

Pivoting

The process of going from one simplex tableau to the next

Product-mix column

The column containing all the variables in a solution in the simplex tableau

Quantity column

The column in a simplex tableau indicating the quantities of the variables that are in a solution