ch 11 resource constraints and linear programming

... 100 80 50 7 20 $356 Formatted Problem and LP Solution For Power Gen Inc. 1 Ch 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. 5 Explanations of the ‘Extension’ Ideas II.  Interdependent projects: projects may prov...

Ngày tải lên: 23/03/2014, 04:20

... 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 Assessment 2. The recent observations of water nutrients were obtained from the litera- ture 3,4 and the measured...

Ngày tải lên: 18/06/2014, 16:20

... divided into three major parts: Linear Programming, Unconstrained Problems, and Constrained Problems. The last two parts together comprise the subject of nonlinear programming. Linear Programming Linear ... are introduced for each time period. In particular, let x i denote the level of stock in the warehouse at the beginning of Linear and Nonlinear Programming Thir...

Ngày tải lên: 27/06/2014, 17:20

... 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 84 In addition to these two WSH options, VBScript gives you two f...

Ngày tải lên: 03/07/2014, 18:20

... fitted by this method (solid) and a line fitted using least squares (dotted): Ji ˇ rí Matoušek Bernd Gärtner Understanding and Using Linear Programming ABC 1.1 A Linear Program 5 (0, 0) x 2 ≥ ... 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 proc...

Ngày tải lên: 03/07/2014, 21:10

... Sensitivity 339 11 .8. Inequality Constraints 3 41 11. 9. Zero-Order Conditions and Lagrange Multipliers 346 11 .10 . Summary 353 11 .11 . Exercises 354 Chapter 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...

Ngày tải lên: 06/08/2014, 15:20

... equations x 1 + x 2 −x 3 = 5 2x 1 −3x 2 +x 3 = 3 −x 1 +2x 2 −x 3 = 1 To obtain an original basis, we form the augmented tableau e 1 e 2 e 3 a 1 a 2 a 3 b 10 0 1 1 15 010 2 313 0 01 12 1 1 and replace e 1 by ... obtain x 1 x 2 x 3 x 4 x 5 x 6 3/ 51/ 5 010 2/ 518 /5 2/ 5 1/ 50 01 3/57/5 1/ 53/ 510 0  1/ 5 1/ 5 Continuing, there results x 1 x 2 x 3...

Ngày tải lên: 06/08/2014, 15:20

... sake of safety. 54 Chapter 3 The Simplex Method x 2 x 3 x 4 x 5 x 6 x 7 b 1 10 1 10 1 12 10 11 2 1 − 210 20−2 Second tableau—phase I 01 11 01 3 12 10 11 2 00 00 11 0 Final tableau—phase I Now ... problem x 2 x 3 x 4 x 5 b 01 11 3 12 10 2 c T 23 11 14 Initial tableau—phase II Transforming the last row appropriately we proceed with: 01 11 3 1 2 10 2 0 −220− 21 Fi...

Ngày tải lên: 06/08/2014, 15:20

... and new  as follows. Variable B 1 Value s 1 1 10 012  2 0 1/ 2 0 1 1/2 0  1 0 1/ 2 1 1 1/ 2 1  2 0 0 0 1 1/2 0 s 1 10−2 −20  2 0 1/ 2 0 1 1/2  3 0 1/ 2 1 1 1/ 2  3 0 0 011  T =  0 4 ... −3000 1 1 1/ 2 1/ 2 0 2 10 1 11 2 30 12 0 8 3/2 1 0 1 1/ 21 10 1 11 2 20 01 110 The optimal solution is x 1 =0, x 2 =1, x 3 =2. The corresponding dual progr...

Ngày tải lên: 06/08/2014, 15:20

... row. a 1 a 2 a 3 ··b 1 12 10 3 213 0 15 −3 −2 50 0−8 1/ 203/2 ··· Second tableau Minimizing the new associated restricted primal by pivoting as indicated we obtain a 1 a 2 a 3 ··b 11 210 3 10 1 11 2 10 12 0−2 1/ 203/2 ... tableau: a 1 a 2 a 3 ··b 011 2 11 10 1 11 2 00 011 0 0 01 ·· Final tableau ∗ 4.7 Reduction of Linear Inequalities 10 1 By subtracting the second equati...

Ngày tải lên: 06/08/2014, 15:20

... +1 =  1+ 1 m 2 1  m 1 /2  1 1 m +1  < exp  1 2m +1 − 1 m +1  =exp  − 1 2m +1   Convergence The ellipsoid method is initiated by selecting y 0 and R such that condition (A1) ... S 1 we have d x +S 1 Xd s =S 1 1−x Then, premultiplying by A and using Ad x =0, we have AS 1 Xd s =AS 1 1−Ax =AS 1 1−b Using d s =−A T d y we have AS 1 XA T...

Ngày tải lên: 06/08/2014, 15:20

... constraint equations in standard form: x 11 +x 12 +···+x 1n =a 1 x 21 +x 22 +···+x 2n =a 2    x m1 +x m2 +···+x mn =a m x 11 +x 21 x m1 =b 1 x 12 + x 22 + x m2 =b 2    x 1n + x 2n + x mn =b n (3) The ... [V3], and Wright [W8]. 16 2 Chapter 6 Transportation and Network Flow Problems 1 2 3 4 (1, 2) (1, 4) (2, 3) (2, 4) (4, 2) 11 11 1 1 1 1 11 Table 6 .1 In...

Ngày tải lên: 06/08/2014, 15:20

... = ⎡ ⎣ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ⎤ ⎦ =  A 11 A 12 A 21 A 22   The resulting submatrices are usually denoted A ij , 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...

Ngày tải lên: 06/08/2014, 15:20

... 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. 4 Explanations of the ‘Extension’ Ideas I.  More Activities and Constraints: this notion deals with more complex resource mixes, and more constraints,...

Ngày tải lên: 31/10/2014, 14:56

... 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 Model Standard Graph 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Number of X units Number of Y units Adding the Linear Constraints...

Ngày tải lên: 31/10/2014, 14:56