Mat 540 Week 9 Quiz 5 - 87427

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Question 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 2 A conditional constraint specifies the conditions under which variables are integers or real variables. Answer True False Question 3 In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1. Answer True False Question 4 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 2 points Question 5 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 2 points 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 cannot be selected. Answer True False 2 points Question 7 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 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 Y1 + Y2 + Y3+ Y4 ? 3 Y1 + Y2 + Y3+ Y4 = 3 Y1 + Y2 + Y3+ Y4 ?3 none of the above 2 points Question 9 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 10 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 + Y4 ? 0 Y1 + Y4 = 0 Y1 + Y4 ? 1 Y1 + Y4 ? 0 2 points Question 11 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 12 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 ? 1 2 points Question 13 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 exactly 2 at least 2 at most 2 none of the above 2 points Question 14 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 2 points Question 15 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 16 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 17 Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ? 136 3x1 + 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 = 56 2 points Question 18 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 ? 1 2 points Question 19 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 2 points Question 20 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
Solution Description

Question 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 2 

A conditional constraint specifies the conditions under which variables are integers or real variables.
 Answer

True

False

Question 3

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

True

False

Question 4

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

2 points  

Question 5

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

2 points  

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 cannot be selected.
Answer

True

False

2 points  

Question 7

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

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this

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