ch 11 resource constraints and linear programming
More Advanced Linear Programming Concepts and Methods pdf
... 100 80 50 7 20 $356 Formatted Problem and LP Solution For Power Gen Inc. 1Ch 12: More Advanced Linear Programming Concepts and Methods Applying Linear Programming to Those Investments in ... goals and constraints, and an appreciation of Linear Programming methodology. 5Explanations of the ‘Extension’ Ideas II. Interdependent projects: projects may provide mutual support and ... solution. 4Explanations of the ‘Extension’ Ideas I. More Activities and Constraints: this notion deals with more complex resource mixes, and more constraints, or combinations of projectsIndivisible...
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WETLAND AND WATER RESOURCE MODELING AND ASSESSMENT: A Watershed Perspective - Chapter 11 pdf
... typical of a shallow water lake. As the larg-est lake in Jianghan Plain, its geological setting is a faulted depression between the â 2008 by Taylor & Francis Group, LLC 140 Wetland and Water ... LLC 138 Wetland and Water Resource Modeling and Assessment2. The recent observations of water nutrients were obtained from the litera-ture3,4 and the measured data (the measured TN and TP ... model can be used to evaluate the impact of land management practices on water, sediment, and agricultural-chemical yields in large, complex basins with a variety of soils and land cover on a time...
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david g luenberger yinyu ye linear and nonlinear programming international series in operati docx
... divided into three major parts: Linear Programming, Unconstrained Problems, and Constrained Problems. The last two parts togethercomprise the subject of nonlinear programming. Linear Programming Linear ... are introduced for each time period. In particular, let xidenote the level of stock in the warehouse at the beginning of Linear and Nonlinear Programming Third Edition David G. Luenberger Stanford ... obtained by setting any two variables to zero and solving for the remaining three. As indicated in Fig. 2.4, each edge of the figurecorresponds to one variable being zero, and the extreme points...
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Microsoft WSH and VBScript Programming for the Absolute Beginner Part 11 ppt
... 86 Microsoft WSH and VBScript Programming for the Absolute Beginner, Second Edition For example, to display a pop-up dialog that displays the OK button without any icon, ... result, as shown in Figure 3.8. Microsoft WSH and VBScript Programming for the Absolute Beginner, Second Edition 84In addition to these two WSH options, VBScript gives you two functions of its ... SectionOption Explicit Microsoft WSH and VBScript Programming for the Absolute Beginner, Second Edition Dim UserInputUserInput = InputBox (“Type a number”, “Square Root Calculator”)MsgBox The square...
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understanding and using linear programming
... fitted by this method (solid) and a linefitted using least squares (dotted): Jiˇrí MatoušekBernd Gärtner Understanding and Using Linear Programming ABC 1.1 A Linear Program 5(0, 0)x2≥ ... substantial linear program in practice often has several thou-sand variables, rather than two or four. A graphical illustration is useful for understanding the notions and procedures of linear programming, ... Linear Programming and Linear AlgebraThe basics of linear algebra can be regarded as a theory of systems of linear equations. Linear algebra considers many other things as well, but systemsof linear...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 1 doc
... Sensitivity 339 11 .8. Inequality Constraints 3 41 11. 9. Zero-Order Conditions and Lagrange Multipliers 346 11 .10 . Summary 353 11 .11 . Exercises 354Chapter 12 . Primal Methods 359 12 .1. Advantage of ... 3 21 11. 2. Tangent Plane 323 11 .3. First-Order Necessary Conditions (Equality Constraints) 326 11 .4. Examples 327 11 .5. Second-Order Conditions 333 11 .6. Eigenvalues in Tangent Subspace 335 11 .7. ... asminimize c 1 x 1 +c2x2+···+cnxnsubject to a 11 x 1 +a 12 x2+···+a1nxn+y 1 =b 1 a 21 x 1 +a22x2+···+a2nxn+y2=b2······am1x 1 +am2x2+···+amnxn+ym=bm and x 1 ...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 2 ppsx
... equationsx 1 + x 2 −x3= 52x 1 −3x 2 +x3= 3−x 1 +2x 2 −x3= 1 To obtain an original basis, we form the augmented tableaue 1 e 2 e3a 1 a 2 a3b 10 0 1 1 15 010 2 313 0 01 12 1 1 and replace e 1 by ... obtainx 1 x 2 x3x4x5x63/ 51/ 5 010 2/ 518 /5 2/ 5 1/ 50 01 3/57/5 1/ 53/ 510 0 1/ 5 1/ 5Continuing, there resultsx 1 x 2 x3x4x5x6 1 1 − 21 0 0 4 1 2 −3 010 2 1 −3 −50 01 1From this last canonical ... 0 2. 2 Examples of Linear Programming Problems 15 c 1 x 1 +c 2 x 2 +···+cnxnsubject to the nutritional constraintsa 11 x 1 +a 12 x 2 +···+a1nxn b 1 a 21 x 1 +a 22 x 2 +···+a2nxn...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 3 ppsx
... sake ofsafety. 54 Chapter 3 The Simplex Methodx2x 3 x4x5x6x7b 1 10 1 10 1 12 10 11 2 1 − 210 20−2Second tableau—phase I 01 11 01 3 12 10 11 200 00 11 0Final tableau—phase INow ... problemx2x 3 x4x5b 01 11 3 12 10 2cT 23 11 14 Initial tableau—phase IITransforming the last row appropriately we proceed with: 01 11 3 1 2 10 20 −220− 21 First tableau—phase II 1/ 20 1/ 21 2 1/ 21 ... yields: 212 104 3 31 0 13 rT−5 −4 30 0−7First tableauPivoting in the column having the most negative bottom row component asindicated, we obtain:0 1 4/ 31 2 /32 11 1 /30 1/ 31 01 4 /30 5 /3 −2Second...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 4 doc
... and new asfollows.Variable B 1 Values 1 1 10 012 20 1/ 2 0 1 1/2 0 1 0 1/ 2 1 1 1/ 2 1 20 0 0 1 1/2 0s 1 10−2 −2020 1/ 2 0 1 1/230 1/ 2 1 1 1/ 230 0 011 T=0 4 ... −3000 1 1 1/ 2 1/ 2 0 2 10 1 11 230 12 0 83/2 1 0 1 1/ 21 10 1 11 220 01 110 The optimal solution is x 1 =0, x2 =1, x3=2. The corresponding dual program ismaximize 4 1 +62subject to 2 1 + ... 2x 1 +4x2+x3+x 4 subject to x 1 +3x2+x 4 4 2x 1 + x2 3x2+4x3+x 4 3x 1 0 i =1 2 3 4 11 . For the linear program of Exercise 10 a) How much can the elements of b = 4 3...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 5 docx
... row.a 1 a2a3··b 1 12 10 3 213 0 15 −3 −2 50 0−8 1/ 203/2 ···Second tableauMinimizing the new associated restricted primal by pivoting as indicated we obtaina 1 a2a3··b 11 210 3 10 1 11 2 10 12 0−2 1/ 203/2 ... tableau:a 1 a2a3··b 011 2 11 10 1 11 200 011 00 01 ··Final tableau ∗4.7 Reduction of Linear Inequalities 10 1By subtracting the second equation from the first and rearranging, we obtainx 1 =2 ... calculate the ratios 1 232obtaining 0= 1 2, and add this multiple ofthe third row to the fourth row to obtain the next tableau.a 1 a2a3··b 11 210 3 10 1 11 2 10 12 0−20 01 ··Third tableauOptimizing...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 6 pptx
... +1 = 1+ 1 m2 1 m 1 /2 1 1 m +1 < exp 1 2m +1 − 1 m +1 =exp− 1 2m +1 ConvergenceThe ellipsoid method is initiated by selecting y0 and R such that condition (A1) ... S 1 we havedx+S 1 Xds=S 1 1−xThen, premultiplying by A and using Adx=0, we haveAS 1 Xds=AS 1 1−Ax =AS 1 1−bUsing ds=−ATdywe haveAS 1 XATdy=b−AS 1 1Thus, ... the minimal-volume ellipsoidcontaining 1/ 2Ek. It is constructed as follows. Define = 1 m +1 =m2m2 1 =2yk 1/ 2 EFig. 5 .1 A half-ellipsoid 13 6 Chapter 5 Interior-Point MethodsãThe...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 7 pps
... constraintequations in standard form:x 11 +x 12 +···+x1n=a 1 x 21 +x22+···+x2n=a2xm1+xm2+···+xmn=amx 11 +x 21 xm1=b 1 x 12 + x22+ xm2=b2x1n+ x2n+ xmn=bn(3)The ... [V3], and Wright [W8]. 16 2 Chapter 6 Transportation and Network Flow Problems 1 234 (1, 2) (1, 4) (2, 3) (2, 4) (4, 2) 11 11 1 1 1 1 11 Table 6 .1 Incidence matrix for exampleClearly, all information ... i =1 2n;j =1 2n tominimizenj =1 ni =1 cijxijsubject tonj =1 xij =1 for i =1 2 n (11 )ni =1 xij =1 for j =1 2 nxij 0 for i = 1 2 nj =1 ...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 11 docx
... =⎡⎣a 11 a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34⎤⎦=A 11 A 12 A 21 A 22 The resulting submatrices are usually denoted Aij, as illustrated.A matrix can be partitioned ... and Qi [S 12] , Tseng [T 12] , and Ye [Y3].15.9 There have been several remarkable applications of SDP; see, for example, Goemans and Williamson [G8], Boyd et al [B 22] , Vandenberghe and Boyd [V2], ... is that part of the closure thatis not in the interior. 522 Appendix B Convex SetsBut, since x0∈H,c =aTx0=aTx1+1−aTx 2 and thus x1 and x 2 ∈H. Hence x1, x 2 ∈T and x0is...
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ch 12 more advanced linear programming concepts and methods
... 1 Ch 12: More Advanced Linear Programming Concepts and Methods Applying Linear Programming to Those Investments in Which The Simplifying Assumptions of Basic ... scale, multiple goals and investment risk.4Explanations of the ‘Extension’ Ideas I. More Activities and Constraints: this notion deals with more complex resource mixes, and more constraints, ... the Hydro scheme is to be adopted. Such a scaled down scheme may not be acceptable. To ensure that projects are either accepted or rejected in their entirety, Mixed Integer Linear Programming...
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ch 11 resource constraints and linear programming
... Ch 11 Resource Constraints and Linear Programming The process of finding an optimum outcome from a set of constrained resources, where the objective function and the constraints ... as linear equations. Drawing the Linear ModelStandard Graph050010001500200025000 500 1000 1500 2000 2500Number of X unitsNumber of Y units Adding the Linear Constraints Standard ... constraint levels. Linear Programming: SummaryUse when an optimum solution is required, from constrained resources.Express the objective function and the constraints as linear equations.Solve...
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