Solution To The LP Relaxation Of A Maximization Integer
The Solution To The Lp Relaxation Of A Maximization Integer Linear
The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Answer True False
A conditional constraint specifies the conditions under which variables are integers or real variables. Answer True False
In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1. Answer True False
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
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
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. Answer True False
If we are solving a 0-1 integer programming problem, the constraint x₁ ≤ x₂ is a __________ constraint. Answer multiple choice mutually exclusive conditional corequisite
The Wiethoff Company has a contract to produce 10,000 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
If we are solving a 0-1 integer programming problem, the constraint x₁ = x₂ is a __________ constraint. Answer multiple choice mutually exclusive conditional corequisite
The Wiethoff Company has a contract to produce 10,000 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. Answer Y₁ + Y₄ ≤ 0 Y₁ + Y₄ = 0 Y₁ + Y₄ ≤ 1 Y₁ + Y₄ ≥
In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer total 0-1 mixed all of the above
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, write the constraint(s) for the second restriction. Answer S₂ + S₅ ≤ 1 S₄ + S₅ ≤ 1 S₂ + S₅ + S₄ + S₅ ≤ 2 S₂ + S₅ ≤ 1, S₄ + S₅ ≤
Assume that we are using a 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
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
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
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
Max Z = 5x₁ + 6x₂ Subject to: 17x₁ + 8x₂ ≤ x₁ + 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 =
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 ≤
Max Z = 3x₁ + 5x₂ Subject to: 7x₁ + 12x₂ ≤ x₁ + 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
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? 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
The Solution To The LP Relaxation Of A Maximization Integer Linear
The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Answer True False
A conditional constraint specifies the conditions under which variables are integers or real variables. Answer True False
In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1. Answer True False
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
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
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. Answer True False
If we are solving a 0-1 integer programming problem, the constraint x₁ ≤ x₂ is a __________ constraint. Answer multiple choice mutually exclusive conditional corequisite
The Wiethoff Company has a contract to produce 10,000 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
If we are solving a 0-1 integer programming problem, the constraint x₁ = x₂ is a __________ constraint. Answer multiple choice mutually exclusive conditional corequisite
The Wiethoff Company has a contract to produce 10,000 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. Answer Y₁ + Y₄ ≤ 0 Y₁ + Y₄ = 0 Y₁ + Y₄ ≤ 1 Y₁ + Y₄ ≥
In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer total 0-1 mixed all of the above
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, write the constraint(s) for the second restriction. Answer S₂ + S₅ ≤ 1 S₄ + S₅ ≤ 1 S₂ + S₅ + S₄ + S₅ ≤ 2 S₂ + S₅ ≤ 1, S₄ + S₅ ≤
Assume that we are using a 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
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
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
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
Max Z = 5x₁ + 6x₂ Subject to: 17x₁ + 8x₂ ≤ x₁ + 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 =
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 ≤
Max Z = 3x₁ + 5x₂ Subject to: 7x₁ + 12x₂ ≤ x₁ + 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
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. 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