Analytics- Chapter 2 Linear programming (LP) Models: Graphical Models

Optimal Solution

The point with the best objective function value (for example, highest profit or lowest cost) within the feasible region is optimal

Feasible Region

The set of points that satisfies all constraints

Proportionality

basic assumption of an LP Model. each term in the Objective Function and Constraints changes in proportion with a change in variable value

Certainty

basic assumption of an LP Model. numbers in the Objective Function and Constraints are known with certainty and do not change during the period studied

Divisibility

basic assumption of an LP Model. the solutions (i.e., the values of the decision variables) need not be in whole numbers. Fractional solutions are accepted.

Additivity

basic assumption of an LP Model. the total revenue, cost and resource usage from all activities equals the sum from the individual activities

product mix problem

decide how much to make of two or more products, objective is to maximize profit, limited resources

Redundant Constraints

do not affect the feasible region. Example: x < or = 10 x < or = 12. second constraint is less restrictive

level curve

the movement of a parallel line to the optimal point

Infeasibility

when no feasible solution exists. example x < or = 10, x > or = 15.

unbounded solution

when nothing prevents the solution from becoming infinitely large, this can only occur for a max problem since a MIN LP solution is bounded by (0,0)

alternate optimal solution

when there is more than one optimal solution, this condition occurs when the level curve falls parallel to, or more specifically ON TOP OF a constraint line, this IS feasbile and is not immediately recognizable in a computer solution

Corner Point Property

An optimal solution must lie at one or more corner points