Which is the correct relationship between IP and its LP relaxation? a. The optimal objective value of LP relaxation is better than that of IP b. The optimal objective value of LP relaxation is worse than that of IP c. IP is easier to solve d. IP can be solved by rounding the optimal solution of the LP relaxation

Which is the correct relationship between IP and its LP relaxation? a. The optimal objective value of LP relaxation is better than that of IP b. The optimal objective value of LP relaxation is worse than that of IP c. IP is easier to solve d. IP can be solved by rounding the optimal solution of the LP relaxation

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.5: Set-covering And Location-assignment Models

Problem 26P

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1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
Finish this statement: The objective function value for ILP problems can never... match the optimal solution to its LP relaxation. be better than the optimal solution to its LP relaxation. be as poor as the optimal solution to its LP relaxation. be worse than the optimal solution to its LP relaxation.
Which of the following is true? 1.Multistart feature in Solver guarantees that the solution obtained from Solver is a global optimal solution. 2.A nonlinear optimization problem can have multiple global optimal solutions. 3.A local optimum for an optimization problem is the best point in the feasible region. 4.There is no guarantee that a solution of a linear programming model obtained from Solver is a global solution.
what will happen if the right hand side value of a constraint in two variable linear programming problems is changed? a. optimal measure of performance may change b. parallel shift must be made in the graph of that constraint c. optimal valued for one or more of the decision variables may change d. all of the above e. none of the above
Which of the following is true regarding the linear programming formulation of a transportation problem that doesn't have any unacceptable routes? The number of constraints is calculated as number of origins times number of destinations. The constraints' left-hand-side coefficients are less than zero. The objective function value is either 0 or 1. The number of variables is calculated as number of origins times number of destinations.
True or False 1. Given three corner points A, B, and C of a linear programming problem, if A is adjacent to B and B is adjacent to C, then A can be determined from C by interchanging exactly two basic and two nonbasic variables. 2. For a set of primary and dual solutions to be feasible, the objective function value of the primary (Z) can never exceed that of the dual (W) no matter which problem is to maximize and which is to minimize. 3. If the current iteration is degenerate, the next iteration will also be degenerate. 4. The optimal (dual) primary solution can be obtained from the dual (primary) optimal tableau.
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Which of the following statement is not true? A. We can get the optimal solution for IP by rounding the optimal solution for LP. B. IP is an extension of LP in which some or all of the decision variables are constrained to be an integer. C. There are three types of IP. They are Pure IP, Mixed IP, and Binary IP. D. The binary variable takes on values of 0 or 1.
Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this…
The linear program Max 3X1 + 2X2 is solved subject to the constraints i) X1 + X2 ≤ 10 ii) 3X1 + X2 ≤ 24 iii) X1 + 2X2 ≤ 16 and iv) non-negativity for both X1 and X2. Which of the following statements is true? A. The optimal solution occurs at the point (6, 6). B. The feasible region has five corner points. C. The optimal solution occurs at (8, 0) and the optimal value is 24. D. The optimal solution value is 41.
Which of the following statements about linear programming is NOT correct? A. Minimization problems are often unbounded inward. B. The iso-cost approach attempts to move the objective function in towards the origin as far as possible. C. The feasible region is determined the same way for a minimization problem as for a maximization problem. D. LP problems can be structured to minimize costs as well as maximize profits. (Don't hand writing solution)