MAT 540 Week 10 Quiz 5

•    Question 1
2 out of 2 points
   
     In a problem involving capital budgeting applications, the 0-1 variables designate the acceptance or rejection of the different projects.
 

•    Question 2
2 out of 2 points
   
     Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.
 

           
•    Question 3
2 out of 2 points
   
     If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.
 

           
•    Question 4
2 out of 2 points
   
     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 5
2 out of 2 points
   
     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.
 

           
•    Question 6
2 out of 2 points
   
     The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.
 

           
•    Question 7
2 out of 2 points
   
     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 8
2 out of 2 points
   
     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           

•    Question 9
2 out of 2 points
   
     If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is
Answer           
   
           
•    Question 10
2 out of 2 points
   
     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           

           
•    Question 11
2 out of 2 points
   
     The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem.
Answer           

•    Question 12
2 out of 2 points
   
     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           

           
•    Question 13
2 out of 2 points
   
     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           

           
•    Question 14
2 out of 2 points
   
     Binary variables are

           
•    Question 15
2 out of 2 points
   
     Max Z = 5x1 + 6x2
Subject to: 17x1 + 8x2 ≤ 136
                  3x1 + 4x2 ≤ 36
                  x1, x2 ≥ 0 and integer
What is the optimal solution?

           
•    Question 16
2 out of 2 points
   
     If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint.
Answer           

           
•    Question 17
2 out of 2 points
   
     If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.

•    Question 18
2 out of 2 points
   
     If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a __________  constraint.
Answer           

•    Question 19
0 out of 2 points
   
     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
 

           
•    Question 20
2 out of 2 points
   
     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