2 Consider the following IP:min z = 6x + 8x2s.t.3x1 + x2 > 4X1 + 2x, > 4X1, X2 2 0; x1, X2 integerThe optimal tableau for this IP's linear programmingrelaxation is given in Table 87. Use the cutting planealgorithm to find the optimal solution. TABLE 87서X2rhs111의 s153|5

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Answered: 2 Consider the following IP: min z =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. A student wants to know the effect of 2 parameter settings (Number of iterations and learning rate) on the computation time of an algorithm. Experiments were carried out by trying 3 different values for each parameter, then seeing the response to computation time. If we know the experimental results as shown in the following figure, what information can we get? Boxplot of Speed (sec) Boxplot of Speed (sec) 0,8 0,8- 0,7 0,7- 0,6 0.6 0,5 0,5- 0,4 0,4- 0,3 0,3- 0,2 0,2- 0,50 learning rate 500 1000 1500 0,05 0,95 Niteration Speed (sec)
IN OCTAVE Use Jacobi's algorithm to solve the following system of equations witha tolerance es =5%
Q6. Consider the following linear program in standard maximization form: -5 max{r1 – x2} subject to -4 X1, 12 a) Use the Simplex Method (as seen in class) to solve the above linear program. Be sure to: o Indicate all slack and artificial variables you introduce. o Indicate the objective S of the extended tableau. o Whenever your tableau is in RRREF, indicate the current solution's values for all vari- ables. o Before pivoting, indicate the entry you plan to convert to the next pivot. o Clearly indicate why you should stop the algorithm and give a precise conclusion. b) Draw the feasible region in a fairly large and well-scaled diagram. Determine the coordi- nates of each vertex and label the vertices of the feasible region in your diagram. c) Based on the graphical approach, describe the optimal solutions of this LP (if any). VI VI AI
According to the Master Theorem, what is the run time of the algorithm described by the function T(n) - 4T () +e(nº")
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital.Max 20x1 + 30x2 + 10x3 + 15x4s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5}xj={1, if location j is selected ; 0, otherwise}Which of the constraints enforces a contingent relationship? A. Constraint 1 B. Constraint 2 C. Constraint 3 D. Constraint 4 E. Constraint 5

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2 Consider the following IP: min z = 6x1 + 8x2 s.t. 3x1 + x2 2 4 X1 + 2x2 > 4 X1, X2 2 0; x1, X2 integer The optimal tableau for this IP's linear programming relaxation is given in Table 87. Use the cutting plane algorithm to find the optimal solution.