06 Jun MAT 540 Week 10 Quiz 5 Set 3 QUESTIONS NEW
Question 1: In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.
Question 2: 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 3: 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 4: 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 5: In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.
Question 6: If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.
Question 7: 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 8: If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is
Question 9: 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 10: 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 11: In a __________ integer model, some solution values for decision variables are integers and others can be non-integer.
Question 12: 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 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 ≤ 1 is a __________ constraint.
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, the constraint for the first restriction is
Question 16: Binary variables are
Question 17: 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 18: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.
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
4×1 + 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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