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Unformatted text preview: 7 Integer Linear Programming MULTIPLE CHOICE 1. Which of the following is the most useful contribution of integer programming? a. finding whole number solutions where fractional solutions would not be appropriate b. using 0-1 variables for modeling flexibility c. increased ease of solution d. provision for solution procedures for transportation and assignment problems ANSWER: b TOPIC: Introduction 2. In a model, x 1 > 0 and integer, x 2 > 0, and x 3 = 0, 1. Which solution would not be feasible? a. x 1 = 5, x 2 = 3, x 3 = 0 b. x 1 = 4, x 2 = .389, x 3 = 1 c. x 1 = 2, x 2 = 3, x 3 = .578 d. x 1 = 0, x 2 = 8, x 3 = 0 ANSWER: c TOPIC: Introduction 3. Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. each of the above is true. ANSWER: a TOPIC: LP relaxation 4. Rounding the solution of an LP Relaxation to the nearest integer values provides a. a feasible but not necessarily optimal integer solution. b. an integer solution that is optimal. c. an integer solution that might be neither feasible nor optimal. d. an infeasible solution. ANSWER: c TOPIC: Graphical solution 5. The solution to the LP Relaxation of a maximization integer linear program provides a. an upper bound for the value of the objective function. b. a lower bound for the value of the objective function. c. an upper bound for the value of the decision variables d. a lower bound for the value of the decision variables ANSWER: a TOPIC: Graphical solution 1 2 Chapter 7 Integer Linear Programming 6. The graph of a problem that requires x 1 and x 2 to be integer has a feasible region a. the same as its LP relaxation. b. of dots. c. of horizontal stripes. d. of vertical stripes. ANSWER: b TOPIC: Graphical solution 7. The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost. ANSWER: a TOPIC: Fixed costs 8. Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation and should be disregarded. d. is most useful for 0 - 1 models. ANSWER: c TOPIC: Sensitivity analysis 9. Let x 1 and x 2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below indicates that project 2 can be done only if project 1 is done? a. x 1 + x 2 = 1 b. x 1 + x 2 = 2 c. x 1- x 2 < d. x 1- x 2 > ANSWER: d TOPIC: Conditional and corequisite constraints 10. Let x 1 , x 2 , and x 3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?...
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- Spring '11