ISE 203 OR I

1. ISE 203 OR I Chapter 5 The Theory of the Simplex Method Asst. Prof. Dr. Nergiz Kasımbeyli

9. x1=0 and x1=4 x2=0 and 2x2=12

22. Fig. 5.3 Not a convex set!

27. Whenever a constraint boundary equation is one of the defining equations for a CP solution, its indicating variable has a value of zero in the augmented form of the problem. • Each such indicating variable is called a nonbasic variable for the corresponding basic solution.

29. Degenerate solution • A BF solution is a basic solution where all m basic variables are nonnegative (≥ 0). • A BF solution is said to be degenerate if any of these m variables equals zero. • Thus, it is possible for a variable to be zero and still be a basic variable for the current BF solution (Another constraint boundary equation is satisfied in addition to its n defining equations).

38. The Matrix Form of Simplex

39. The Matrix Form of Simplex

47. Fundamental Insight All you need to know is B-1 and cbB-1. You can calculate these from the initial tableau. or You can read them directly off the final tableau.

48. Fundamental Insight We replace cBB-1 with y*; and B-1 with S*

49. Fundamental Insight y* plays a very special role. These are shadow prices. We will often write the final tableau like this. We can use the fundamental insight for sensitivity analysis.

50. Apply Fundamental Insight • Here is part of the final Tableau for Wyndor • Use the fundamental insight to find the values of the decision variables and the profit.