Mat540 Quiz 5 Week - 9

Question 1
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 2
In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.
Answer
True
False
2 points 
Question 3
If we are solving a 0-1 integer programming problem, the constraint x1 ? x2 is a conditional constraint.
Answer
True
False
2 points 
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
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.
Answer
True
False
2 points 
Question 6
A conditional constraint specifies the conditions under which variables are integers or real variables.
Answer
True
False
2 points 
Question 7
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 1, x2 + x5 ≤ 1 
x1 - x5 ≤ 1 1, x2 - x5 ≤ 1 
2 points 
Question 8
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
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
S1 + S3 + S7  ≥ 1
S1 + S3 + S7 ≤1
S1 + S3 + S7 = 2
S1 + S3 + S7 ≤ 2
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 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 11
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 12
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 13
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 14
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 15
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 16
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 17
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 18
Binary variables are
Answer
any integer value
any continuous value
any negative integer value
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

 

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