MAT 540 WEEK 10 QUIZ 5 LATEST
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MAT 540 Week 10 Quiz 5 Latest
MAT540
MAT 540 Week 10 Quiz 5 Latest
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.
Question 2
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.
Question 3
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.
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.
Question 5
Question 6
Rounding non-integer solution values up to the nearest integer
value will result in an infeasible solution to an integer linear programming
problem.
Question 7
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.
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 a constraint to ensure that if machine 4 is used, machine
1 will not be used.
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, write the constraint(s)
for the second restriction
Question 10
Binary variables are
Question 11
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
Question 12
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.
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.
Question 14
In a 0-1 integer programming model, if the constraint x1-x2 ? 0,
it means when project 2 is selected, project 1 __________ be selected.
Question 15
Max Z = 5×1 + 6×2
Subject to: 17×1 + 8×2 ? 136
3×1 + 4×2 ? 36
x1, x2 ? 0 and integer
What is the optimal solution?
Question 16
If we are solving a 0-1 integer programming problem, the
constraint x1 = x2 is a __________ constraint.
Question 17
In a __________ integer model, some solution values for decision
variables are integers and others can be non-integer.
Question 18
Question 19
Max Z = 3×1 + 5×2
Subject to: 7×1 + 12×2 ? 136
3×1 + 5×2 ? 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
Question 20
Consider the following integer linear programming problem
Max Z = 3×1 + 2×2
Subject to: 3×1 + 5×2 ? 30
5×1 + 2×2 ? 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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