mat540 – Quiz – 5: Week – 9 ( Graded 40/40 )

Question 1

1.                                 

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

Answer[removed]  True 
[removed]  False

  Question 2

1.                                 

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.
 

Answer[removed]  True 
[removed]  False

  Question 3

1.                                 

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

Answer[removed]  True 
[removed]  False

  Question 4

1.                                 

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[removed]  True 
[removed]  False

  Question 5

1.                                 

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

Answer[removed]  True 
[removed]  False

  Question 6

1.                                 

A conditional constraint specifies the conditions under which variables are integers or real variables. 
 

Answer[removed]  True 
[removed]  False

  Question 7

1.                                 

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

Answer

[removed]

 

always optimal and feasible

[removed]

 

sometimes optimal and feasible

[removed]

 

always optimal but not necessarily feasible

[removed]

 

never optimal and feasible

  Question 8

1.                                 

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

Answer

[removed]

 

multiple choice

[removed]

 

mutually exclusive

[removed]

 

conditional

[removed]

 

corequisite

  Question 9

1.                                 

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

Answer

[removed]

 

S2 +S5 ≤ 1

[removed]

 

S4 +S5 ≤ 1

[removed]

 

S2 +S5 + S4 +S5 ≤ 2

[removed]

 

S2 +S5 ≤ 1,  S4 +S5 ≤ 1

  Question 10

1.                                 

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

Answer

[removed]

 

greater than or equal to

[removed]

 

less than or equal to

[removed]

 

equal to

[removed]

 

different than 
 

  Question 11

1.                                 

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

[removed]

 

Y1 + Y2 + Y3+ Y4 ≤ 3

[removed]

 

Y1 + Y2 + Y3+ Y4 = 3

[removed]

 

Y1 + Y2 + Y3+ Y4 ≥3

[removed]

 

none of the above 
 

  Question 12

1.                                 

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

[removed]

 

x1 + x2 + x5 ≤ 1

[removed]

 

x1 + x2 + x5 ≥1

[removed]

 

x1 + x5 ≤ 1,  x2 + x5 ≤ 1

[removed]

 

x1 – x5 ≤ 1,  x2 – x5 ≤ 1

  Question 13

1.                                 

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

[removed]

 

Y1 + Y4 ≤ 0

[removed]

 

Y1 + Y4 = 0

[removed]

 

Y1 + Y4 ≤ 1

[removed]

 

Y1 + Y4 ≥ 0

  Question 14

1.                                 

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?

Answer

[removed]

 

x1 = 6, x2 = 4, Z = 54

[removed]

 

x1 = 3, x2 = 6, Z = 51

[removed]

 

x1 = 2, x2 = 6, Z = 46

[removed]

 

x1 = 4, x2 = 6, Z = 56

  Question 15

1.                                 

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

[removed]

 

can also

[removed]

 

can sometimes

[removed]

 

can never

[removed]

 

must also

  Question 16

1.                                 

Binary variables are

Answer

[removed]

 

0 or 1 only

[removed]

 

any integer value

[removed]

 

any continuous value

[removed]

 

any negative integer value

  Question 17

1.                                 

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

[removed]

 

S1 + S3 + S7 ≥ 1

[removed]

 

S1 + S3 + S7 ≤1

[removed]

 

S1 + S3 + S7 = 2

[removed]

 

S1 + S3 + S7 ≤ 2

  Question 18

1.                                 

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

Answer

[removed]

 

multiple choice

[removed]

 

mutually exclusive

[removed]

 

conditional

[removed]

 

corequisite

  Question 19

1.                                 

Consider the following integer linear programming problem 
 
Max Z =      3x 1  + 2x 2 
Subject to:   3x 1  + 5x 2   ≤ 30 
                    4x 1  + 2x 2   ≤ 28 
                    x 1   ≤ 8 
                    x 1  , x 2   ≥ 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[removed]

  Question 20

1.                                 

Consider the following integer linear programming problem 
 
Max Z =      3x 1  + 2x 2 
Subject to:   3x 1  + 5x 2   ≤ 30 
                    5x 1  + 2x 2   ≤ 28 
                    x 1   ≤ 8 
                    x 1  ,x 2   ≥ 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