Math540 Wk10 Quiz 5

Math540 Wk10 Quiz 5

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Quiz 5

Question 1

2 out of 2 points

	In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.   Answer

Question 2

2 out of 2 points

	If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.   Answer

Question 3

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 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 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 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

	In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer

Question 9

2 out of 2 points

	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. Answer

Question 10

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 the constraint that indicates they can purchase no more than 3 machines. Answer

Question 11

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 12

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 13

0 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 14

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 15

2 out of 2 points

	Binary variables are Answer

Question 16

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 17

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 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, write the constraint(s) for the second restriction Answer

Question 19

2 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 (twenty-five) would be written 25   Answer
	Case Sensitivity

Question 20

2 out of 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. 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