Assignment

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.
True
false

Question 2
A conditional constraint specifies the conditions under which variables are integers or real variables.
True
False

Question 3
In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.
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.
True
False

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.
True
False

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.
True
False

Question 7
If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________ constraint.
multiple choice
mutually exclusive
conditional
corequisite

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.
Y1 + Y2 + Y3+ Y4 ≤ 3
Y1 + Y2 + Y3+ Y4 = 3
Y1 + Y2 + Y3+ Y4 ≥3
none of the above

Question 9
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.
multiple choice
mutually exclusive
conditional
corequisite

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.
Y1 + Y4 ≤ 0
Y1 + Y4 = 0
Y1 + Y4 ≤ 1
Y1 + Y4 ≥ 0

Question 11
In a __________ integer model, some solution values for decision variables are integers and others can be non-integer.
total
0 - 1
Mixed
all of the above

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
S2 +S5 ≤ 1
S4 +S5 ≤ 1
S2 +S5 + S4 +S5 ≤ 2
S2 +S5 ≤ 1, S4 +S5 ≤ 1

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.
exactly 2
at least 2
at most 2
none of the above

Question 14
The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.
greater than or equal to
less than or equal to
equal to
different than

Question 15
If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is
always optimal and feasible
sometimes optimal and feasible
always optimal but not necessarily feasible
never optimal and feasible

Question 16
If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint.
multiple choice
mutually exclusive
conditional
corequisite

Question 17
Max Z = 5x1 + 6x2
Subject to: 17x1 + 8x2 ≤ 136
3x1 + 4x2 ≤ 36
x1, x2 ≥ 0 and integer
What is the optimal solution?
x1 = 6, x2 = 4, Z = 54
x1 = 3, x2 = 6, Z = 51
x1 = 2, x2 = 6, Z = 46
x1 = 4, x2 = 6, Z = 56

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?
x1 + x2 + x5 ≤ 1
x1 + x2 + x5 ≥1
x1 + x5 ≤ 1, x2 + x5 ≤ 1
x1 - x5 ≤ 1, x2 - x5 ≤ 1

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 will be an integer. Please give your as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

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 will be an integer. Please give your as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25.