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Unformatted text preview: rresponding to each basic feasible soluWon. Also, there is at least one bfs corresponding to each extreme point in the feasible region. 4.2 – Preview of the Simplex Algorithm Labor Constraint
40 B
Feasible Region 30 E 20 Leather Constraint 10 Both inequaliWes are saWsﬁed in the shaded area. The extreme points are of the feasible region are B, C, E, and F. D 50 max z = 4x1 + 3x2 s.t. x1 + x2 + s1 = 40 2x1 + x2 + s2 = 60 x1, x2, s1, s2 ≥ 0 60 The relaWonship between extreme points and basic feasible soluWons outlined in Theorem 2, is seen in the Leather Limited problem. The LP (with slack variables) was: X2 C
F 10 20 30 A
40 50 X1 4.2 – Preview of the Simplex Algorithm The table above shows the correspondence between the basic feasible soluWons to the LP and the extreme points of the feasible region. The basic feasible soluWons to the standard form of the LP correspond in a natural fashion to the LP s extreme points. 4.2 – Preview of the Simplex Algorithm Adjacent Basic Feasible SoluCons
For any LP with m constraints, two basic feasible soluWons are said to be adjacent if their sets of basic variables have m – 1 basic variables in common.
For example in the Leather Limited LP on the previous slide, the bfs corresponding to point E is adjacent to the bfs corresponding to point C. These points share (m – 1 = 2 ‐ 1 = 1) one basic variable, x1. Points E (BV = {x1,x2}) and F (BV = {s1,s2}) are not adjacent since they share no basic variables. IntuiWvely, two basic feasible soluWons are adjacent if they both lie...
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This note was uploaded on 09/20/2011 for the course ENG 300 taught by Professor Albin during the Fall '11 term at Rutgers.
 Fall '11
 Albin
 Ode

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