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mat540 - Quiz - 5: Week - 9 (Graded 40/40)

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Question;Question 11. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.AnswerTrueFalseQuestion 21. In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 - x2? 0 implies that if project 2 is selected, project 1 can not be selected.AnswerTrueFalseQuestion 31. The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.AnswerTrueFalseQuestion 41. If we are solving a 0-1 integer programming problem with three decision variables, the constraintx1 +x2? 1 is a mutually exclusive constraint.AnswerTrueFalseQuestion 51. If we are solving a 0-1 integer programming problem, the constraintx1?x2 is a conditional constraint.AnswerTrueFalseQuestion 61. A conditional constraint specifies the conditions under which variables are integers or real variables.AnswerTrueFalseQuestion 71. If the solution values of a linear program are rounded in order to obtain an integer solution, the solution isAnsweralways optimal and feasiblesometimes optimal and feasiblealways optimal but not necessarily feasiblenever optimal and feasibleQuestion 81. If we are solving a 0-1 integer programming problem, the constraintx1 =x2 is a __________ constraint.Answermultiple choicemutually exclusiveconditionalcorequisiteQuestion 91. You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 andS3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2orS4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, write the constraint(s) for the second restrictionAnswerS2 +S5? 1S4 +S5? 1S2 +S5 + S4 +S5? 2S2 +S5? 1, S4 +S5? 1Question 101. The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.Answergreater than or equal toless than or equal toequal todifferent thanQuestion 111. The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Write the constraint that indicates they can purchase no more than 3 machines.AnswerY1 + Y2 + Y3+ Y4? 3Y1 + Y2 + Y3+ Y4 = 3Y1 + Y2 + Y3+ Y4?3none of the aboveQuestion 121. In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?Answerx1 + x2 + x5? 1x1 + x2 + x5?1x1 + x5? 1, x2 + x5? 1x1 - x5? 1, x2 - x5? 1Question 131. The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.AnswerY1 + Y4? 0Y1 + Y4 = 0Y1 + Y4? 1Y1 + Y4? 0Question 141. Max Z = 5x1 + 6x2Subject to: 17x1 + 8x2? 136 3x1 + 4x2? 36 x1, x2? 0 and integerWhat is the optimal solution?Answerx1 = 6, x2 = 4, Z = 54x1 = 3, x2 = 6, Z = 51x1 = 2, x2 = 6, Z = 46x1 = 4, x2 = 6, Z = 56Question 151. In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected.Answercan alsocan sometimescan nevermust alsoQuestion 161. Binary variables areAnswer0 or 1 onlyany integer valueany continuous valueany negative integer valueQuestion 171. You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 andS3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2orS4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed.Assuming that Si is a binary variable, the constraint for the first restriction isAnswerS1 + S3 + S7? 1S1 + S3 + S7?1S1 + S3 + S7 = 2S1 + S3 + S7? 2Question 181. If we are solving a 0-1 integer programming problem, the constraintx1?x2 is a __________ constraint.Answermultiple choicemutually exclusiveconditionalcorequisiteQuestion 191. Consider the following integer linear programming problemMax Z = 3x1 + 2x2Subject to: 3x1 + 5x2? 30 4x1 + 2x2? 28 x1? 8 x1, x2? 0 and integerFind the optimal solution.What is the value of the objective function at the optimal solution.Note: The answer will be an integer.Please give your answer as an integer without any decimal point.For example, 25.0 (twenty-five) would be written 25AnswerQuestion 201. Consider the following integer linear programming problemMax Z = 3x1 + 2x2Subject to: 3x1 + 5x2? 30 5x1 + 2x2? 28 x1? 8 x1,x2? 0 and integerFind the optimal solution.What is the value of the objective function at the optimal solution.Note: The answer will be an integer.Please give your answer as an integer without any decimal point.For example, 25.0 (twenty-five) would be written 25

 

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