Math 540 Week 9 Quiz 5

download Question 1 1. 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. Answer True False 2 points Question 2 1. 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 â‰¤ 0 implies that if project 2 is selected, project 1 can not be selected. Answer True False 2 points Question 3 1. In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. Answer True False 2 points Question 4 1. A conditional constraint specifies the conditions under which variables are integers or real variables. Answer True False 2 points Question 5 1. 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 2 points Question 6 1. If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 +x2 + x3 â‰¤ 3 is a mutually exclusive constraint. Answer True False 2 points Question 7 1. 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 8 1. 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 1. 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 x1 x1 1 x1

+ x2 + x5 ≤ 1 + x2 + x5 ≥1 + x5 ≤ 1, x2 + x5 ≤ - x5 ≤ 1, x2 - x5 ≤ 1 2 points

Question 10 1. 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 11 1. 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 12 1. 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. Answer Y1 Y1 Y1 Y1

+ + + +

Y4 Y4 Y4 Y4

≤ = ≤ ≥

0 0 1 0 2 points

Question 13 1. 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 14 1. 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 15 1. 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 2 points Question 16 1. Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? Answer x1 x1 x1 x1

= = = =

6, 3, 2, 4,

x2 = x2 = x2 = x2 =

4, 6, 6, 6,

Z= Z= Z= Z=

54 51 46 56 2 points

Question 17 1. In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected. Answer must always can sometimes can never A and B 2 points Question 18 1. 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 S2or 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 S1 S1 S1

+ + + +

S3 S3 S3 S3

+ + + +

S7 S7 S7 S7

≥1 ≤1 =2 ≤2

2 points Question 19 1. Consider the following integer linear programming problem Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 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 Answer 2 points Question 20 1. 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 Question 1 2 out of 2 points 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. Answer Question 2 2 out of 2 points 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 Question 3 2 out of 2 points In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects. Answer Question 4 2 out of 2 points A conditional constraint specifies the conditions under which variables are integers or real variables. Answer

Question 5 2 out of 2 points The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Answer Question 6 2 out of 2 points If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 â‰¤ 3 is a mutually exclusive constraint. Answer Question 7 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Answer Question 8 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Answer Question 9 2 out of 2 points 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 Question 10 2 out of 2 points If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is Answer Question 11 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 + x2 â‰¤ 1 is a __________ constraint. Answer Question 12 2 out of 2 points 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. Answer Question 13 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________ constraint. Answer Question 14 2 out of 2 points 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 Question 15 2 out of 2 points In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer Question 16 2 out of 2 points Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? Answer Question 17 2 out of 2 points In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected. Answer Question 18 2 out of 2 points 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 Question 19 0 out of 2 points Consider the following integer linear programming problem Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 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 (twentyfive) would be written 25 Answer

Question 20 2 out of 2 points 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 (twentyfive) would be written 25 Answer

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