Lecture4

5 x r 6 x 2x r i 3 6 i 7 x y rrrrrr

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Unformatted text preview: , +.-cl = 1 x, .J. .x, ..r, 2 0 .. Reducing Model Complexity A Special Case l l From the sotution (x415 x2=615 x4=1 x+=0) x1 and XI are both basic and part of the original objective futtCtiOtI Find the current state of the objective function by substitution ,? = 4X, +I, l Consider the following LP Minimize sublect to z = x, + 2.~~ + 3x, 3.~, +A.~, 25 5.x, + x1 + 6.s, = 7 8.x, + 9r, t 2 s, ,x, , .K) 2 0 I z---r \ - 18-’ 1 5 EM-602 I QM-710 (NJ) Lecture 4 Page 4-6 Reducing Model Complexity Reducing Model Complexity A Special Case (Page 2) A Special Case (Page 3) 3 - .r, - 2.5 - 3.r, - J/R, - A/R, = 0 3.5 f-lx, + .r, = 5 h, +x2 +(1x, + R, = 7 8.5 + 9.r, - .Y, + R1 = 2 .~,..r:..~,..r,..r~.R,.RI 20 .r, = j.R, = l.R, = 2 We may observe that in this model Decision variable x2 appears in one and only one constraint The constraint is an equality constraint We may therefore Force the value of Decision variable x2 to be equal to the RHS of constraint Eliminate the need for one Artiftcial variable Reducing Model Complexity Assignments for Lecture 4 A Special Case (Page 4) (due in 1 week) The problem in Standard Form is: l l l l l =-.r,-Z.r,-3-r,-.\/R,=O 3.~, +-Lx, + x, = 5 5x, f.TI + 6Xj = 7 8.5 + 9.~; -x! + R, = 2 .~,..~...~,..)c,..T..R, 2 0 _r, = j..rl = 7.R, = 2 l l Homework Problem 33 Homework Problem #3 l l Handout Problem #3 (solve problem by both M-Technique and Two-Phase Technique) Problems 3-5, 3-22(a), 3-22(d) Read Sections 3.53.6 (a) Determine the maximum number of Extrema (b) Identify all feasible Extreme points (c) Find the Optimal Basic Feasible Solution Sdve ustng the Big-M simplex method Solve uslng the Two-Phase Technique Minimize .z = 80x, +60x, subject to 0.20x, +0.32x. < 025 .r, +.I+, = I x,.x. > 0 EM-602 / QM-710 (NJ) Lecture 4 Page 4-7 .. Homework Problem 3-22 Solve by M-Technique (a) Masmize z = ZS, + 3.~ - 5.x, (d) Minmlize z = As, - 8-v: + 3.q subject to s, + 2x, + s, = 7 h, -5.x, +s, 2 IO .I., .s> .s, 2 0 EM-602 I QM-710 (NJ) Lecture 4 Page 4-8...
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