MAT/540 MAT540 MAT 540 WEEK 10 QUIZ 5

Binary variables are

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________  constraint.

In a __________ integer model, some solution values for decision variables are integers and others can be non-integer.

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint.

The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.

In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected.

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

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint.

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

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

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.

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
 

Consider the following integer linear programming problem
 
Max Z =      3x₁ + 2x₂
Subject to:   3x₁ + 5x₂ ≤ 30
                    4x₁ + 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
 

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.
 

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.
 

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.
 

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.
 

If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.
 

The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.