Mat 540 Week 9 Quiz 5

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 below
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 below

 

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