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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Consider the following LP: Minimize z - 4x1 + x2 subject to 3x1 + x2 = 30 4x, + 3x2 2 60 X1 + 2x2 = 40 X1, X2 2 0 The starting solution consists of artificial x4 and xs for the first and second constraints and slack x, for the third constraint. Using M = 100 for the artificial variables, the optimal tableau is given as Basic X2 X3 X6 Solution -98.6 -100 -2 34 1 4 -2 4 X2 1 2 .6 18 X3 1 -1 1 10 Write the associated dual problem, and determine its optimal solution in two ways.
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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
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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
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
Consider the simplex tableau below which has arisen in a maximization problem. Identify the next entering variable and binding row. X2 X3 X4 X5 X6 R.H.S. Basic var. 1 1 -1 3 -2 20 z = 20 1 1 1 1 X6 = 3 X2 = 7 O x3 and row 1; O x4 and row 13; O xs and row 2; O none of the above.

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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.