Suppose the primal LP is a maximization problem, and it has a feasible solution with objective value 500. Is it possible the dual has a feasible solution withobjective value 300?YesO NoQUESTION 2Suppose the dual LP is a minimization problem, and it has a feasible solution. Is it possible the primal is unbounded?YesO NoQUESTION 3Suppose the dual LP is a minimization problem, and it has an optimal solution with objective value 1000. Is it possible the primal is unbounded?O YesNo

For the following question we use strong duality theorem which states that, The strong duality…

Answered: Suppose the primal LP is a maximization…

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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An integer programming (maximization) problem was first solved as a linear programming problem, and the objective function value (profit) was $253.67. The two decision variables (X, Y) in the problem had values of X = 12.45 and Y = 32.75. If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem? 1) X = 12, Y = 322) The objective function value must be less than $253.673) X = 12, Y = 334) The objective function value will be greater than $253.675) The objective function value would still be equal to $253.67
Solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x − 3y subject to 2x + y ≥ 8 y ≤ 7 x ≥ 0, y ≥ 0 p = (x,y) =
The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 6x1 + 3x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 (a) Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ------ to -------- (b) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ----- to -------- (c) Compute the dual value for the first constraint, second constraint & third constraint
29-30. The shaded region in the given figure above illustrates an unbounded feasible region. Which of the following is true? 1. The maximum value for the objective function does not exist in an unbounded feasible region. II. If the objective function is Min Z=x+y, then it's maximum is 25 at (25,0). III. If the objective function is Max Z=-x+2y, then it's minimum is O at (25,0). IV. Unbounded feasible regions have either maximum or minimum value. (0,24) 50 -10 -20 O A. I B. II C. I and II D. III and IV 20 10 0 -10 (12) 10 (15.5) (25.0) 40
29-30. The shaded region in the given figure above illustrates an unbounded feasible region. Which of the following is true? 1. The maximum value for the objective function does not exist in an unbounded feasible region. II. If the objective function is Min Z=x+y, then it's maximum is 25 at (25,0). III. If the objective function is Max Z=-x+2y, then it's minimum is O at (25,0). IV. Unbounded feasible regions have either maximum or minimum value. (0.24) 50 -20 -10 A. I B. II C. I and II D. III and IV 10 . -10 (12) 10 (15,5) (25.0) 40
In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of op solutions is possible. Give a very brief explanation to justify why your rule should work. mal Using your rule, do one more iteration to obtain a second optimal solution.
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x + y subject to x + 2y 2 20 2x + 2y ≤ 20 2x + y 2 20 x ≥ 0, y ≥ 0. p = = (L (x, y) =
Q1\A) Put True or False for the following questions: 1. A solution of linear programing problem is called feasible if it satisfies all of the constraints. 2. Every linear program has a function called objective function. 3. Level line is the set of all points where the objective function takes no specific value. 4. The dual problem of primal problem is also primal. 5. We compute a new tableau if we get the optimal solution from the simplex method.
Consider the following LP model: max 10x1 + 12x2 + s.t. x1 2x1 2x1 + + + X2 + 2x2 + 2x3 + 2x3 2x2 + X3 X 12x3 ≤20 0 Use the simplex method and find the optimal solution for this problem. (You need to determine the objective value, the basic and non-basic variables and their values.)

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