Mat 540 Week 9 Quiz 5

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. 

Answer

True

false

 2 points   

Question 2  

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

Answer 

True

False 

Question 3 

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

Answer 

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. 

Answer 

True

False 

2 points   

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. 

Answer 

True

False 

2 points   

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.

Answer 

True

False 

2 points   

Question 7 

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

Answer 

multiple choice

mutually exclusive

conditional

corequisite

2 points   

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.

Answer 

Y1 + Y2 + Y3+ Y4 ≤ 3

Y1 + Y2 + Y3+ Y4 = 3

Y1 + Y2 + Y3+ Y4 ≥3

none of the above 

 2 points   

Question 9   

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

Answer 

multiple choice

mutually exclusive

conditional

corequisite

2 points   

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.

Answer 

Y1 + Y4 ≤ 0

Y1 + Y4 = 0

Y1 + Y4 ≤ 1

Y1 + Y4 ≥ 0

2 points   

Question 11 

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

Answer 

total

0 – 1

Mixed

all of the above

2 points   

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

Answer 

S2 +S5 ≤ 1

S4 +S5 ≤ 1

S2 +S5 + S4 +S5 ≤ 2

S2 +S5 ≤ 1,  S4 +S5 ≤ 1

2 points   

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.

Answer 

exactly 2

at least 2

at most 2

none of the above

2 points   

Question 14 

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

Answer 

greater than or equal to

less than or equal to

equal to

different than 

 2 points   

Question 15

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

Answer 

always optimal and feasible

sometimes optimal and feasible

always optimal but not necessarily feasible

never optimal and feasible

2 points   

Question 16 

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

Answer 

multiple choice

mutually exclusive

conditional

corequisite

2 points   

Question 17 

Max Z = 5x1 + 6x2 

Subject to: 17x1 + 8x2 ≤ 136 

3x1 + 4x2 ≤ 36 

x1, x2 ≥ 0 and integer 

What is the optimal solution?

Answer 

x1 = 6, x2 = 4, Z = 54

x1 = 3, x2 = 6, Z = 51

x1 = 2, x2 = 6, Z = 46

x1 = 4, x2 = 6, Z = 56

2 points   

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?

Answer 

x1 + x2 + x5 ≤ 1

x1 + x2 + x5 ≥1

x1 + x5 ≤ 1,  x2 + x5 ≤ 1

x1 - x5 ≤ 1,  x2 - x5 ≤ 1

2 points   

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 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 below

2 points   

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 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 below

Show more >
  • mastersolution
    mastersolution
    53 orders completed
    $15.00
    ANSWER
    Tutor has posted answer for $15.00. See answer's preview

    ******** 1 ***

    ******** to *** LP ********** ** * maximization integer linear ******* provides ** upper ***** for *** value ** the ********* ********* *******

    *****

    ******

    *

    points ******** 2

    * *********** **********

    specifies *** ********** ***** ***** ********* are ******** ** real variables ******* ***** ******

    ********

    3

    In

    * *****

    ******* ***** **** ******** ****** *** ******** variables *** ******* *** ****** are **** or ** ******* ***** ******

    Question

    **

    **

    ** ***

    solving * 0-1 integer *********** ******* **** ***** ******** ********* *** ********** ** * ** **** * is * mutually ********* *********** Answer ***** ******

    *

    ******

    Question

    5 ******** ***********

    ******** values

    ** ** *** ******* ******* ***** **** ****** ** ** infeasible ******** ** ** integer linear *********** ******** ******* ***** False *

    ******

    ********

    **

    In * ***

    integer programming

    ******* ********* * ******* ********* application ****** xj * 1 ** project * ** ******** ** * ********** the ********** ** - x2 **** implies **** ** project 2 ** ******** ******* * ****** ** ********* ******* ***** ****** * ******

    Question

    **

    **

    ** are *******

    * ***

    integer *********** problem the ********** ** **** ** ** * ********** *********** ******* multiple ******* ******** ********** ************

    corequisite

    * points

    ******** 8

    ***

    Wiethoff

    ******* *** a

    ******** **

    produce ***** garden hoses for * ******** ******** *** 4 different ******** that *** produce this **** of hose ******* ***** ******** are **** ********* ************* and *** ********* ************ their specifications are *** the ***** Write *** ********** **** indicates **** ***

    ********

    **

    **** **** * ********* Answer ** * ** * *** ** **** **

    Y1

    + ** * Y3+ ** * ** **

    + ** * Y3+ ** ≥3 none **

    *** above 2 points ******** 9 **

    we *** ******* a

    *** ******* ***********

    ******* *** **********

    ** * x2 is * ********** *********** ******* ******** ******* ******** ********** ************ corequisite * ****** ******** ***

    ***

    ******** Company

    *** *

    ********

    to

    ******* 10000 ******

    ***** for

    * ******** ******** *** * ********* machines **** *** produce this kind of **** Because ***** ******** are **** ********* manufacturers and use ********* technologies ***** ************** are *** the ***** ***** * ********** ** ensure **** ** ******* * ** used machine

    *

    ****

    ***

    ** ***** ******* ** * ** **** ** + ** * ** * Y4 **** ** **

    *

    ** **** 2 ****** Question

    *** ** a __________ integer

    ***** some solution values ***

    ******** variables *** integers ***

    ****** *** be

    ************ *******

    total – 1 ****** *** ** *** ****** * points ******** ** You **** been asked ** ******

    **

    least

    * out

    **

    7 possible sites ***

    *** *********** *********

    **** **** as

    ** ** ** S4 ** ** *** S7 *** ************ ***** *********** * ********** sites S1 *** ** **** prevent *** from exploring **** *** *********** * Evaluating ***** ** *** **

    will prevent *** **** assessing **** S5 *********** * ** *** the ***** **

    ***** * should ** ********* Assuming

    that ** ** * binary ******** ***** ***

    ************* for *** ****** restriction Answer ** *** **** ** ** ***

    **** ** ** *** + ** *** ≤ 2 ** *** ≤ 1 **

    ***

    **** ** * ******

    Question ** ****** ****

    ** are ***** *** ******* programming *****

    ** ***** * capital ********* ******* and xj

    * * **

    ******* * **

    ******** *** ** * ********** The constraint *** * ** * ** * ** **** ** ***** **** __________ *** of the * ******** must be ********* *******

    ******* 2 at least 2 ** **** ** **** of *** ****** * points ******** 14 *** ******** to *** ****** ***********

    **********

    ** a

    minimization ******* ****

    always ** __________

    *** value ** ***

    ******* *********** ************

    problem Answer

    ******* **** or ***** *** **** **** or ***** *** equal *** different than 2 ****** ******** *** ** the solution values **

    *

    ****** program *** rounded **

    ***** to ****** an *******

    solution the

    ******** ***

    Answer ****** optimal

    *** *********

    ********* optimal *** ********* ****** ******* *** *** necessarily ********* ***** ******* and ********* * ****** ******** *** ** we

    are

    ******* a 0-1 *******

    *********** ******* *** constraint

    ** * ** ≤ * **

    * __________ *********** *******

    multiple ******* mutually

    exclusive ************

    corequisite * ****** Question *** Max * = *** * **** Subject *** 17x1 * *** **** 136 *** +

    4x2

    **** ***

    x1 **

    ***

    ******** **** **

    *** *******

    solution? ******* ** * * **

    * * Z * 54 ** *

    * ** * * *

    * *** ** * *

    ** * * * *

    ***

    ** * 4 ** * * * * ***

    2 points ******** 18 In * capital ********* problem

    ** ****** ******* * or project * ** ********

    then ******* 5 ****** ** selected ***** ** the

    ************ ****** below

    ********* ****** ****

    *********** Answer ** + ** + x5 **** ** ** + ** * ** ≥1 ** + ** **** * x2 * ** ≤ ** ** * x5 **** 1

    x2

    * ** **** 1 * ****** ********

    19 *** Z * *** *

    **** Subject *** *** * **** ≤ 136 *** *

    *** **** 36 ** ** **** and ******** Find the

    ******* ******** What

    is ***

    value of *** objective function **

    the optimal ******** Note: The ****** ****

    ** ** integer ****** ****

    **** ****** as an *******

    ******* *** ******* ***** *** example *** ************* would be ******* *** ****** ****** * points ******** *** ******** *** ********* ******* ****** *********** ******** *** * = 3x1 + **** ******* *** *** * *** **** *** *** + *** ≤

    28 x1

    **** ** **

    ** ****

    *** ******** Find *** ******* solution ****

    ** *** ***** of *** *********

    function ** the ******* ******** ***** ***

    ****** **** ** ** *******

    ****** **** ****

    ****** ** ** integer *******

    ***

    ******* ***** For ******* *** (twenty-five) ***** ** written *** ****** *****

    Click here to download attached files:

    mat_540_week_9_quiz_5.doc

    Buy

Learn more effectively and get better grades!

Do my homework