06 Jun MAT 540 Week 10 Quiz 5 Set 1 QUESTIONS NEW Question 1: Rounding non-integer solution values up to t
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.
Question 2: The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.
Question 3: If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.
Question 4: A conditional constraint specifies the conditions under which variables are integers or real variables.
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.
Question 6: If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program.
Question 7: 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.
Question 8: In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected.
Question 9: 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.
Question 10: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint.
Question 11: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.
Question 12: If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is
Question 13: If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint.
Question 14: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________ constraint.
Question 15: Binary variables are
Question 16: In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected.
Question 17: The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.
Question 18: In a __________ integer model, some solution values for decision variables are integers and others can be non-integer.
Question 19: Max Z = 3×1 + 5×2
Subject to: 7×1 + 12×2 ≤ 136
3×1 + 5×2 ≤ 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
Question 20: Consider the following integer linear programming problem
Max Z = 3×1 + 2×2
Subject to: 3×1 + 5×2 ≤ 30
5×1 + 2×2 ≤ 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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