Engineering Optimization: Theory and Practice, Fourth Edition
3.9 Simplex Algorithm 143 Figure 3.14 Flowchart for finding the optimal solution by the simplex algorithm. ...
144 Linear Programming I: Simplex Method Example 3.4 MaximizeF=x 1 + 2 x 2 +x 3 subject to 2 x 1 +x 2 −x 3 ≤ 2 − 2 x 1 +x 2 − 5 ...
3.9 Simplex Algorithm 145 Thusx 2 enters the next basic set. To obtain the new canonical form, weselect the pivot elementa′′rssu ...
146 Linear Programming I: Simplex Method form as shown below: Basic Variables b ′′ i/a ′′ isfor variables x 1 x 2 x 3 x 4 x 5 x ...
3.9 Simplex Algorithm 147 SOLUTION Introducing the slack variablesx 3 ≥ and 0 x 4 ≥ , the given system of 0 equations can be wri ...
148 Linear Programming I: Simplex Method At this stage we notice thatx 3 has the most negative cost coefficient and hence itshou ...
3.9 Simplex Algorithm 149 Result of pivoting: x 3 8 0 1 −^1200 1,500 x 2 104 1 0 101 0 0 200 x 5 108 0 0 − 103 1 0 300 −f 0 0 0 ...
150 Linear Programming I: Simplex Method are known, an infinite number of nonbasic (optimal) feasible solutions can be obtained ...
3.10 Two Phases of the Simplex Method 151 1.Arrange the original system of Eqs. (3.32) so that all constant termsbi are positive ...
152 Linear Programming I: Simplex Method where di= − (a 1 i+a 2 i+ · · · +ami), i= 1 , 2 ,... , n (3.39) −w 0 = − (b 1 +b 2 + · ...
3.10 Two Phases of the Simplex Method 153 Figure 3.15 Flowchart for the two-phase simplex method. ...
154 Linear Programming I: Simplex Method Figure 3.15 (continued) the complete array of equations can be written as 3 x 1 − 3 x 2 ...
3.10 Two Phases of the Simplex Method 155 This array can be rewritten as a canonical system with basic variables asy 1 , y 2 , − ...
156 Linear Programming I: Simplex Method Step 4At this stage we notice that the present basic feasible solution does not contain ...
3.11 MATLAB Solution of LP Problems 157 4 x 1 +x 2 +x 3 ≤ 6 xi≥ 0 ; i= 1 , 2 , 3 SOLUTION Step 1Express the objective function i ...
158 Linear Programming I: Simplex Method cgiterations: [] message: 'Optimization terminated.' References and Bibliography 3.1 G. ...
Review Questions 159 3.8 What is a basis? 3.9 What is a pivot operation? 3.10 What is the difference between a convex polyhedron ...
160 Linear Programming I: Simplex Method (u)The optimum solution of an LP problem cannot contain slack variables in the basis. ( ...
Problems 161 Figure 3.16 Reservoir in an irrigation district. wet and dry seasons, respectively. Of the total amount of water re ...
162 Linear Programming I: Simplex Method 3.6 What elementary operations can be used to transform 2 x 1 +x 2 +x 3 = 9 x 1 +x 2 +x ...
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