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# • Question 1 If we are solving a 0-1 integer programming problem, the constraint x1 ? x2 is a conditional constraint. • Question 2 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 3 A conditional constraint specifies the conditions under which variables are integers or real variables. • Question 4 Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. • Question 5 In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. • Question 6 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. • Question 7 Binary variables are • Question 8 Max Z = 5×1 + 6×2 Subject to: 17×1 + 8×2 ? 136 3×1 + 4×2 ? 36 x1, x2 ? 0 and integer What is the optimal solution? • Question 9 If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. • Question 10 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 11 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 12 The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem. • Question 13 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? • Question 14 If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is • Question 15 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 • 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. • Question 17 If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. • Question 18 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. • 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

• Question 1
If we are solving a 0-1 integer programming problem, the constraint x1 ? x2 is a conditional constraint.

• Question 2
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 3
A conditional constraint specifies the conditions under which variables are integers or real variables.

• Question 4
Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

• Question 5
In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.

• Question 6
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.

• Question 7
Binary variables are

• Question 8
Max Z = 5×1 + 6×2
Subject to: 17×1 + 8×2 ? 136
3×1 + 4×2 ? 36
x1, x2 ? 0 and integer
What is the optimal solution?

• Question 9
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

• Question 10
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 11
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 12
The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.

• Question 13
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?

• Question 14
If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

• Question 15
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

• 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.

• Question 17
If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint.

• Question 18
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.

• 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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