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##### Strayer MAT540 week 10 quiz 5

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Question;Question 1;Rounding non-integer solution values up to the nearest;integer value will result in an infeasible solution to an integer linear;programming problem.;Answer;True;False;2 points;Question 2;In a mixed integer model, some solution values for decision;variables are integer and others are only 0 or 1.;Answer;True;False;2 points;Question 3;If we are solving a 0-1 integer programming problem, the;constraint x1? x2 is a conditional constraint.;Answer;True;False;2 points;Question 4;If we are solving a 0-1 integer programming problem with;three decision variables, the constraint x1 + x2? 1 is a mutually exclusive;constraint.;Answer;True;False;2 points;Question 5;If we are solving a 0-1 integer programming problem with;three decision variables, the constraint x1 + x2 + x3? 3 is a mutually;exclusive constraint.;Answer;True;False;2 points;Question 6;A conditional constraint specifies the conditions under;which variables are integers or real variables.;Answer;True;False;2 points;Question 7;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?;Answer;x1 + x2 + x5? 1;x1 + x2 + x5?1;x1 + x5? 1, x2 + x5;? 1;x1 - x5? 1, x2 - x5;? 1;2 points;Question 8;If we are solving a 0-1 integer programming problem, the;constraint x1 + x2 = 1 is a __________ constraint.;Answer;multiple choice;mutually exclusive;conditional;corequisite;2 points;Question 9;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 and S3 will prevent you from exploring site S7.;Restriction 2.;Evaluating sites S2 or;S4 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 is;Answer;S1 + S3 + S7? 1;S1 + S3 + S7?1;S1 + S3 + S7 = 2;S1 + S3 + S7? 2;2 points;Question 10;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.;Answer;Y1 + Y2 + Y3+ Y4? 3;Y1 + Y2 + Y3+ Y4 = 3;Y1 + Y2 + Y3+ Y4?3;none of the above;2 points;Question 11;If we are solving a 0-1 integer programming problem, the;constraint x1 = x2 is a __________ constraint.;Answer;multiple choice;mutually exclusive;conditional;corequisite;2 points;Question 12;If we are solving a 0-1 integer programming problem, the;constraint x1? x2 is a;constraint.;Answer;multiple choice;mutually exclusive;conditional;corequisite;2 points;Question 13;In a 0-1 integer programming model, if the constraint x1-x2;= 0, it means when project 1 is selected, project 2 __________ be selected.;Answer;can also;can sometimes;can never;must also;2 points;Question 14;If the solution values of a linear program are rounded in;order to obtain an integer solution, the solution is;Answer;always optimal and feasible;sometimes optimal and feasible;always optimal but not necessarily feasible;never optimal and feasible;2 points;Question 15;Max Z = 5x1 + 6x2;Subject to: 17x1 + 8x2? 136;3x1;+ 4x2? 36;x1;x2? 0 and integer;What is the optimal solution?;Answer;x1 = 6, x2 = 4, Z = 54;x1 = 3, x2 = 6, Z = 51;x1 = 2, x2 = 6, Z = 46;x1 = 4, x2 = 6, Z = 56;2 points;Question 16;Assume that we are using 0-1 integer programming model to;solve a capital budgeting problem and xj = 1 if project j is selected and xj =;0, otherwise.;The constraint (x1 + x2 + x3 + x4? 2) means that;out of the 4 projects must be selected.;Answer;exactly 2;at least 2;at most 2;none of the above;2 points;Question 17;The solution to the linear programming relaxation of a;minimization problem will always be __________ the value of the integer;programming minimization problem.;Answer;greater than or equal to;less than or equal to;equal to;different than;2 points;Question 18;Binary variables are;Answer;0 or 1 only;any integer value;any continuous value;any negative integer value;2 points;Question 19;Max Z = 3x1 + 5x2;Subject to: 7x1 +;12x2? 136;3x1 + 5x2? 36;x1, x2? 0 and integer;Find 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;Answer;2 points;Question 20;Consider the following integer linear programming problem;Max Z = 3x1 + 2x2;Subject to: 3x1 +;5x2? 30;5x1;+ 2x2? 28;x1;? 8;x1,x2? 0 and integer;Find 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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