6 Show that (for a max problem) if the ith primal constraintis a z constraint, then the optimal value of the ith dualvariable may be written as (coefficient of a, in optimalrow 0) – M.

For maximization problem. We have to show that is the ith Primal constraint is a ≥ constraint, then…

Answered: 6 Show that (for a max problem) if the…

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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4.14 The following two inequalities are simultaneous constraints of some binary IP problem. a¡yi +a2y2 +a3y3 + a4Y4
In a linear programming problem, the binding constraints for the optimal solution are: 2x1 + 25x2 ≤ 74 14x1 + 48x2 ≤ 108 What value from the 2nd constraint can the slope of the objective function not exceed in order for the current optimal solution point to remain optimal? Round your solution to 2 decimal places. thats all the data provided^
Q3. The final optimal tableau of a maximization linear programming problem with three constraints of type (S) and two unknowns (x1, x2) is given below. Slack variables are denoted by sı, s2, and s3 for the respective constraints. Find the value of objective function z in two different ways by using the primal-dual relationships (Hint: The Strong Duality Theorem). Basis X2 S2 RHS X1 S3 3 2 1 1 -1 X2 1 1 X1 1 -1
2. a) Mathematical model and 1. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Z max = 3x, + 2x2 Cj 3 -M Constraints: S1 A1 RHS X1 X2 V1 X¡ +2x, <6 Xj 2 7 저20, x2 20 X1 3 1 2 1 Aj -M -2 -1 -1 1 1 Zj 3 6+2M 3+M M -M 18-M C;-Zj 0 -4-2M -3-M -M b) Mathematical model and 2. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Cj 1 -M Z max = x +2x2 Constraints: X1 X2 V1 A1 RHS X2 2 1 1 4 X1 +x, 21 Vị -1 1 -1 1 3 x2 <4 2 2 8. Zj 1 저20, x, 20 Cj-Zj -M -2
4.5. Let { dj, ... , d, } be directions of unboundedness for the constraints Ax = b, x > 0. %3D Prove that k d = ) a;d; with a; > 0 i=1 is also a direction of unboundedness for these constraints.
Question2: Zmin=3x1+4x2+5x3 2x1+x2+2x3<=120 x1+x2+x3=100 x1,x2>=0 and x3 are unconstrained Which of the following is true about the dual cycle of the given linear programming model? 1-)Dual model should have 2 dual variables (v1) and 3 dual constraints. 2-) The linear programming model given is in canonical (appropriate) form. 3-)All constraints of the dual model should be written as <=. 4-) The objective function of the dual model is Qmin. 5-) The sign of the second dual variable of the dual model must be unconstrained.
List the corner points for the following collection of constraints of a linear programming problem. x ≤ 13 4x + 6y224 X20 y20 a. (0,4), (6, 0), (13,0) b. (0, 0), (6, 0), (0, 13) c. (0, 0), (0, 4), (13,0) d. (0,4), (0, 24), (13, 0) e. (0, 0), (6, 0), (13,0) O O
2
Determine the inward column and the outer row for the following linear programming problem Max (Z) = 3 X + 5Y Constraints: 2X +3YS 30 5X +4Y<60 By Condition X, Y20 Find the product using Pascal's rule (a + b)°
min x1 + x2 s.t. 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1, x2 ≥ 0 For the LP problem above, which are the binding constraints? 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1 ≥ 0 x2 ≥ 0
true/false 1) The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question. 2) Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs. 3) generally, The optimal solution to an integer linear program is less sensitive to the constraint coefficients then is a linear program. 4) Multiple choice constraints involve binary variables
(4) Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra Page B: Learn1600andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…

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6 Show that (for a max problem) if the ith primal constraint is a z constraint, then the optimal value of the ith dual variable may be written as (coefficient of a, in optimal row 0) – M.