Chapter 7 (quanti)

1. Chapter 7 Introduction to Linear Programming

8. Example of Linear Programming Problem Sign Restrictions If the decision variable can assume only nonnegative values, the sign restriction x i ≥ 0 is added. If the variable can assume both positive and negative values, the decision variable x i is unrestricted in sign (often abbreviated urs ). The coefficients of the constraints are often called the technological coefficients . The number on the right-hand side of the constraint is called the constraint’s right-hand side (or rhs ).

12. Assumptions of Linear Programming 1. The contribution of each variable to the left-hand side of each constraint is proportional to the value of the variable. 2. The contribution of a variable to the left-hand side of each constraint is independent of the values of the variable. Each LP constraint must be a linear inequality or linear equation has two implications:

17. Graphical Solution to a 2-Variable LP Any point on or in the interior of the five sided polygon DGFEH(the shade area) is in the feasible region . Isoprofit line for maximization problem ( Isocost line for minimization problem )is a set of points that have the same z-value

19. Two type of Constraints A constraint is nonbinding if the left-hand side and the right-hand side of the constraint are unequal when the optimal values of the decision variables are substituted into the constraint.

21. Alternative or Multiple Solutions Any point (solution) falling on line segment AE will yield an optimal solution with the same objective value

22. no feasible solution No feasible region exists Some LPs have no solution. Consider the following formulation:

23. Unbpunded LP The constraints are satisfied by all points bounded by the x 2 axis and on or above AB and CD. There are points in the feasible region which will produce arbitrarily large z-values (unbounded LP) .