# Quiz 6: Integer Linear Programming

Statistics

Q 1Q 1

An integrality condition indicates that some (or all) of the
A) RHS values for constraints must be integer
B) objective function coefficients must be integer
C) constraint coefficients must be integer
D) decision variables must be integer

Free

Multiple Choice

D

Q 2Q 2

Variables, which are not required to assume strictly integer values are referred to as
A) strictly non-integer.
B) continuous.
C) discrete.
D) infinite.

Free

Multiple Choice

B

Q 3Q 3

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as
A) quickest solution method.
B) LP satisficing.
C) LP relaxation.
D) LP approximation.

Free

Multiple Choice

C

Q 4Q 4

How is an LP problem changed into an ILP problem?
A) by adding constraints that the decision variables be non-negative.
B) by adding integrality conditions.
C) by adding discontinuity constraints.
D) by making the RHS values integer.

Free

Multiple Choice

Q 5Q 5

The LP relaxation of an ILP problem
A) always encompasses all the feasible integer solutions to the original ILP problem.
B) encompasses at least 90% of the feasible integer solutions to the original ILP problem.
C) encompasses different set of feasible integer solutions to the original ILP problem.
D) will not contain the feasible integer solutions to the original ILP problem.

Free

Multiple Choice

Q 6Q 6

The objective function value for the ILP problem can never
A) be as good as the optimal solution to its LP relaxation.
B) be as poor as the optimal solution to its LP relaxation.
C) be worse than the optimal solution to its LP relaxation.
D) be better than the optimal solution to its LP relaxation.

Free

Multiple Choice

Q 7Q 7

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?
A) An upper bound.
B) A lower bound.
C) An alternative optimal solution.
D) An additional constraint for the ILP problem.

Free

Multiple Choice

Q 8Q 8

For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?
A) An upper bound.
B) A lower bound.
C) An alternative optimal solution.
D) An additional constraint for the ILP problem.

Free

Multiple Choice

Q 9Q 9

In the B & B algorithm, B & B stands for
A) Brooks and Baker
B) Best Bound
C) Best Branch
D) Branch and Bound

Free

Multiple Choice

Q 10Q 10

The B & B algorithm solves ILP problems
A) by solving for each variable separately.
B) by solving for the integer variables first.
C) by solving a series of LP problems.
D) by solving smaller ILP problems.

Free

Multiple Choice

Q 11Q 11

How are general integrality requirements indicated in the Excel Risk Solver Platform (RSP)?
A) Specifying the INT option for the appropriate changing cells.
B) Specifying the INT option for the constraint rows.
C) Adding additional RHS values to constraints.
D) Choosing the BIN setting in the Value field in the Solver Parameters dialog box.

Free

Multiple Choice

Q 12Q 12

What does the Risk Solver Platform (RSP) default integer tolerance factor of 0 accomplish?
A) Stops B & B after 100% of all solutions are examined.
B) Stops B & B when any feasible ILP solution is 0% from the current ILP solution.
C) Stops B & B when the true optimal integer solution has been found.
D) Stops B & B when no more than 0% of the changing cells have integer values.

Free

Multiple Choice

Q 13Q 13

Which of the following are potential pitfalls of using a non-zero integer tolerance factor in the Risk Solver Platform (RSP)?
A) No assurance the returned solution is optimal.
B) No assurance the returned solution is integer.
C) The true optimal solution may be worse than the returned solution.
D) There are no pitfalls to consider since the Solver will obtain solutions quicker.

Free

Multiple Choice

Q 14Q 14

How is the integer tolerance factor set in the Risk Solver Platform (RSP)?
A) By adding a constraint for the decision variables who's RHS is the desired suboptimality level.
B) By choosing the optimal option in the RSP Options dialog box.
C) By choosing the 100% Precision field in the RSP Options dialog box.
D) By entering the desired tolerance factor value in the Integer Tolerance field of RSP.

Free

Multiple Choice

Q 15Q 15

Which of the following is not a benefit of using binary variables?
A) With only 2 values, Solver can work faster.
B) Binary variables are useful in selection problems.
C) Binary variables can replace some IF() conditions.
D) Binary variables can enforce logical conditions.

Free

Multiple Choice

Q 16Q 16

How are binary variables specified in the Risk Solver Platform (RSP)?
A) By replacing RHS values in constraints with 0 or 1.
B) By specifying changing cells as INTEGER and as non-negative.
C) By specifying changing cells as BINARY in the Variable Type/Bound area of RSP.
D) By selecting Assume Binary Model in the RSP Options dialog box.

Free

Multiple Choice

Q 17Q 17

An ILP problem has 5 binary decision variables. How many possible integer solutions are there to this problem?
A) 5
B) 10
C) 25
D) 32

Free

Multiple Choice

Q 18Q 18

Consider the constraint X

_{3}+ X_{4}+ X_{5}+ X_{6}+ X_{7} 27 Representing Air Express' Monday minimum worker requirement. Why was a "" used versus an "="? A) The "" is needed to accommodate workers held over from Sunday. B) Solver only accepts "" constraints. C) The "" is less restrictive. D) The "=" will always produce an infeasible constraint.Free

Multiple Choice

Q 19Q 19

A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected?
A) X

_{1}+ X_{2}+ X_{3}+ X_{4}= 2 B) X_{1}+ X_{2}+ X_{3}+ X_{4} 2 C) X_{1}+ X_{2}+ X_{3}+ X_{4} 2 D) X_{1}+ X_{2}+ X_{3}+ X_{4} 0Free

Multiple Choice

Q 20Q 20

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?
A) X

_{1}+ X_{2}+ X_{3}+ X_{4}= 1 B) X_{1}+ X_{2}+ X_{3}+ X_{4} 1 C) X_{1}+ X_{2}+ X_{3}+ X_{4} 1 D) X_{1}+ X_{2}+ X_{3}+ X_{4} 0Free

Multiple Choice

Q 21Q 21

If a company produces Product 1, then it must produce at least 150 units of Product 1. Which of the following constraints enforces this condition?
A) X

_{1} 150Y_{1}B) X_{1} 150Y_{1} 0 C) X_{1}Y_{1} 150 D) X_{1} 150 + Y_{1}Free

Multiple Choice

Q 22Q 22

A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition?
A) X

_{1} M_{2}Y_{2}B) X_{1} M_{2}X_{2}C) X_{1} M_{1}Y_{1}, X_{1} Y_{1}X_{2}D) X_{1} X_{2}Free

Multiple Choice

Q 23Q 23

A company must invest in project 1 in order to invest in project 2. Which of the following constraints ensures that project 1 will be chosen if project 2 is invested in?
A) X

_{1}+ X_{2}= 0 B) X_{1}+ X_{2}= 1 C) X_{1} X_{2} 0 D) X_{1} X_{2} 0Free

Multiple Choice

Q 24Q 24

If a company selects Project 1 then it must also select either Project 2 or Project 3. Which of the following constraints enforces this condition?
A) X

_{1} X_{2} X_{3} 0 B) X_{1}+ (X_{2} X_{3}) 0 C) X_{1}+ X_{2}+ X_{3} 2 D) X_{1} X_{2} X_{3} 0Free

Multiple Choice

Q 25Q 25

If a company selects either of Project 1 or Project 2 (or both), then either Project 3 or Project 4 (or both) must also be selected. Which of the following constraints enforce this condition?
A) X

_{1}+ X_{2} 2(X_{3}+ X_{4}) B) X_{1}+ X_{2} X_{3}+ X_{4}C) X_{1} X_{3}= X_{2} X_{4}D) X_{1}+ X_{2}+ X_{3}+ X_{4} 2Free

Multiple Choice

Q 26Q 26

The setup cost incurred in preparing a machine to produce a batch of product is an example of a
A) fixed charge.
B) random charge.
C) sunk cost.
D) variable cost.

Free

Multiple Choice

Q 27Q 27

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as
A) decision variables.
B) production cost constraint coefficients.
C) variable costs.
D) marginal costs.

Free

Multiple Choice

Q 28Q 28

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as
X

_{i}= the amount of product i produced Y_{i}= 1 if X_{i}> 0 and 0 if X_{i}= 0 What is the objective function for this problem? A) MAX: 17 X_{1}+ 21 X_{2}B) MAX: 17 X_{1}+ 21 X_{2} 60 Y_{1} 80 Y_{2}C) MIN: 17 X_{1}+ 21 X_{2} 60 Y_{1} 80 Y_{2}D) MIN: 60 Y_{1}+ 80 Y_{2}Free

Multiple Choice

Q 29Q 29

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as
X

_{i}= the amount of product i produced Y_{i}= 1 if X_{i}> 0 and 0 if X_{i}= 0 Which of the following constraints creates the link between setting up to produce A's and making some A's for this problem? A) X_{1} 16Y_{1}B) X_{1} Y_{1}= 0 C) X_{1} 18Y_{1}> 0 D) = if(X_{1}> 0, Y_{1}= 1, Y_{1}= 0)Free

Multiple Choice

Q 30Q 30

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. The decision variables are defined as
X

_{i}= the amount of product i produced Y_{i}= 1 if X_{i}> 0 and 0 if X_{i}= 0 What is the appropriate value for M_{1}in the linking constraint for product A? A) 2 B) 3 C) 16 D) 12Free

Multiple Choice

Q 31Q 31

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. What is the appropriate formula to use in cell E8 of the following Excel implementation of the ILP model for this problem?
A) =SUMPRODUCT(B5:C5,B7:C7) SUMPRODUCT(B8:C8,B14:C14)
B) =SUMPRODUCT(B8:C8,B14:C14) SUMPRODUCT(B5:C5,B7:C7)
C) =SUMPRODUCT(B5:C5,B7:C7) B8:C8
D) =SUMPRODUCT(B5:C5,B7:C7) SUMPRODUCT(B8:C8,B15:C15)

Free

Multiple Choice

Q 32Q 32

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. What is the appropriate formula to use in cell B15 of the following Excel implementation of the ILP model for this problem?
A) =B5 MIN($E$11/B11, $E$11/C11)*B14
B) =B5 MIN($E$11/B11, $E$12/B12)
C) =B5 $E$12/B12*B14
D) =B5 MIN($E$11/B11, $E$12/B12)*B14

Free

Multiple Choice

Q 33Q 33

A company is planning next month's production. It has to pay a setup cost to produce a batch of X

_{4}'s so if it does produce a batch it wants to produce at least 100 units. Which of the following pairs of constraints show the relationship(s) between the setup variable Y_{4}and the production quantity variable X_{4}? A) X_{4} M_{4}Y_{4}, X_{4} 100 B) X_{4} M_{4}Y_{4}, X_{4}= 100 Y_{4}C) X_{4} M_{4}Y_{4}, X_{4} 100 Y_{4}D) X_{4} M_{4}Y_{4}, X_{4} 100 Y_{4}Free

Multiple Choice

Q 34Q 34

A company will be able to obtain a quantity discount on component parts for its three products, X

_{1}, X_{2}and X_{3}if it produces beyond certain limits. To get the X_{1}discount it must produce more than 50 X_{1}'s. It must produce more than 60 X_{2}'s for the X_{2}discount and 70 X_{3}'s for the X_{3}discount. How many binary variables are required in the formulation of this problem? A) 3 B) 6 C) 9 D) 12Free

Multiple Choice

Q 35Q 35

A company will be able to obtain a quantity discount on component parts for its three products, X

_{1}, X_{2}and X_{3}if it produces beyond certain limits. To get the X_{1}discount it must produce more than 50 X_{1}'s. It must produce more than 60 X_{2}'s for the X_{2}discount and 70 X_{3}'s for the X_{3}discount. How many decision variables are required in the formulation of this problem? A) 3 B) 6 C) 9 D) 12Free

Multiple Choice

Q 36Q 36

A company will be able to obtain a quantity discount on component parts for its three products, X

_{1}, X_{2}and X_{3}if it produces beyond certain limits. To get the X_{1}discount it must produce more than 50 X_{1}'s. It must produce more than 60 X_{2}'s for the X_{2}discount and 70 X_{3}'s for the X_{3}discount. Which of the following pair of constraints enforces the quantity discount relationship on X_{3}? A) X_{31} M_{3}Y_{3}, X_{32} 50Y_{3}B) X_{31} M_{3}Y_{3}, X_{31} 50 C) X_{32} (1/50)X_{31}, X_{31} 50 D) X_{32} M_{3}Y_{3}, X_{31} 50Y_{3}Free

Multiple Choice

Q 37Q 37

A wedding caterer has several wine shops from which it can order champagne. The caterer needs 100 bottles of champagne on a particular weekend for 2 weddings. The first supplier can supply either 40 bottles or 90 bottles. The relevant decision variable is defined as
X

_{1}= the number of bottles supplied by supplier 1 Which set of constraints reflects the fact that supplier 1 can supply only 40 or 90 bottles? A) X_{1} 40 Y_{11}, X_{1} 90(1 Y_{11}) B) X_{1}= 40Y_{11}+ 90Y_{12}, Y_{11}+ Y_{12} 1 C) X_{1}= 40Y_{1}+ 90(1 Y_{1}), Y_{1}= 0 OR 1 D) X_{1}= 40Y_{11}+ 90Y_{12}, Y_{11}+ Y_{12}= 1Free

Multiple Choice

Q 38Q 38

The branch-and-bound algorithm starts by
A) relaxing all the integrality conditions in an ILP and solving the resulting LP problem.
B) relaxing all the RHS values in an ILP and solving the resulting LP problem.
C) solving two LP problems in which X

_{1}is set at 0 and 1 respectively. D) determining the most likely RHS values and solving for them.Free

Multiple Choice

Q 39Q 39

Any integer variable in an ILP that assumes a fractional value in the optimal solution to the relaxed LP problem can be designated
A) a diverging variable.
B) a branching variable.
C) a bifurcating variable.
D) a splitting variable.

Free

Multiple Choice

Q 40Q 40

The optimal relaxed solution for an ILP has X

_{1}= 3.6 and X_{2}= 2.9. If we branch on X_{1}, what constraints must be added to the two resulting LP problems? A) X_{1} 3, X_{1} 4 B) X_{1}= 4 C) 3 X_{1}, X_{1} 4 D) X_{1} 3, X_{1} 4Free

Multiple Choice

Q 41Q 41

A sub-problem in a B & B is solved and found infeasible. Should the B & B algorithm continue further analysis on this candidate problem?
A) Yes, a feasible solution may be found when additional constraints are added.
B) Yes, removing a constraint in further analysis may restore feasibility.
C) No, adding more constraints will not restore problem feasibility.
D) No, the result cannot occur so re-examine the formulation and start over.

Free

Multiple Choice

Q 42Q 42

A small town wants to build some new recreational facilities. The proposed facilities include a swimming pool, recreation center, basketball court and baseball field. The town council wants to provide the facilities which will be used by the most people, but faces budget and land limitations. The town has $400,000 and 14 acres of land. The pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. Also the council has only enough flat land to build the basketball court or the baseball field. The daily usage and cost of the facilities (in $1,000) are shown below.
Formulate the ILP for this problem.

Free

Essay

Q 43Q 43

A small town wants to build some new recreational facilities. The proposed facilities include a swimming pool, recreation center, basketball court and baseball field. The town council wants to provide the facilities which will be used by the most people, but faces budget and land limitations. The town has $400,000 and 14 acres of land. The pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. Also the council has only enough flat land to build the basketball court or the baseball field. The daily usage and cost of the facilities (in $1,000) are shown below.
Based on this ILP formulation of the problem and the indicated optimal solution what values should go in cells B5:G12 of the following Excel spreadsheet?

Free

Essay

Q 44Q 44

A small town wants to build some new recreational facilities. The proposed facilities include a swimming pool, recreation center, basketball court and baseball field. The town council wants to provide the facilities which will be used by the most people, but faces budget and land limitations. The town has $400,000 and 14 acres of land. The pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. Also the council has only enough flat land to build the basketball court or the baseball field. The daily usage and cost of the facilities (in $1,000) are shown below.
Based on this ILP formulation of the problem what formulas should go in cells F5:F12 of the following Excel spreadsheet?

Free

Essay

Q 45Q 45

A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director.
Define the ILP formulation for this capital budgeting problem.

Free

Essay

Q 46Q 46

Exhibit 6.1
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.1. What values would you enter in the Risk Solver Platform (RSP) task pane for the above Excel spreadsheet?
Objective Cell:
Variables Cells:
Constraints Cells:

Free

Essay

Q 47Q 47

Exhibit 6.1
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.1. What formulas should go in cells D8:H8 and D11:H11 of the above Excel spreadsheet?

Free

Essay

Q 48Q 48

Exhibit 6.1
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.1. What formula should go in cell D15 of the above Excel spreadsheet?

Free

Short Answer

Q 49Q 49

A company has four projects, numbered 1 through 4. If any project is selected for implementation, each lower-numbered project must also be selected for implementation. Formulate the constraints to enforce these conditions.

Free

Essay

Q 50Q 50

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below.
Formulate the ILP for this problem.

Free

Essay

Q 51Q 51

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below.
Based on this ILP formulation of the problem and the indicated optimal integer solution values what values should go in cells B5:F12 of the following Excel spreadsheet?

Free

Essay

Q 52Q 52

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below.
Based on this ILP formulation of the problem what formulas should go in cells E5:E12 of the following Excel spreadsheet?

Free

Essay

Q 53Q 53

A company wants to build a new factory in either Atlanta or Columbia. It is also considering building a warehouse in whichever city is selected for the new factory. The following table shows the net present value (NPV) and cost of each facility. The company wants to maximize the net present value of its facilities, but it only has $15 million to invest.
Formulate the ILP for this problem.

Free

Essay

Q 54Q 54

A company wants to build a new factory in either Atlanta or Columbia. It is also considering building a warehouse in whichever city is selected for the new factory. The following table shows the net present value (NPV) and cost of each facility. The company wants to maximize the net present value of its facilities, but it only has $15 million to invest.
Based on this ILP formulation of the problem and the indicated optimal solution what values should go in cells B6:G14 of the following Excel spreadsheet?

Free

Essay

Q 55Q 55

A company wants to build a new factory in either Atlanta or Columbia. It is also considering building a warehouse in whichever city is selected for the new factory. The following table shows the net present value (NPV) and cost of each facility. The company wants to maximize the net present value of its facilities, but it only has $16 million to invest.
Based on this ILP formulation of the problem and the indicated optimal solution what formulas should go in cells F6:F14 of the following Excel spreadsheet?

Free

Essay

Q 56Q 56

A company wants to build a new factory in either Atlanta or Columbia. It is also considering building a warehouse in whichever city is selected for the new factory. The following table shows the net present value (NPV) and cost of each facility. The company wants to maximize the net present value of its facilities, but it only has $16 million to invest.
Based on this ILP formulation of the problem what is the optimal solution to the problem?

Free

Essay

Q 57Q 57

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.
Formulate the ILP for this problem.

Free

Essay

Q 58Q 58

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.
Based on this ILP formulation of the problem what values should go in cells B5:G24 of the following Excel spreadsheet?
Let X

_{i}= 1 if truck located in zone i, 0 otherwiseFree

Essay

Q 59Q 59

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.
Based on this ILP formulation of the problem what formulas should go in cells B13:B16, B20:E20, F20, and F23:F24 of the following Excel spreadsheet?
Let X

_{i}= 1 if truck located in zone i, 0 otherwiseFree

Essay

Q 60Q 60

A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are:
Formulate the ILP for this problem.

Free

Essay

Q 61Q 61

A company needs to hire workers to cover a 7 day work week. Employees work 5 consecutive days with 2 days off. The demand for workers by day of the week and the wages per shift are:
Based on this ILP formulation of the problem and the optimal solution (X

_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}) = (2, 10, 16, 6, 14, 8, 6) what values should go in cells B5:J13 of the following Excel spreadsheet?Free

Essay

Q 62Q 62

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table:
Formulate the ILP for this problem.

Free

Essay

Q 63Q 63

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table:
Based on this ILP formulation of the problem and the solution (X

_{1}, X_{2}, X_{3}, X_{4}) = (1, 1, 0, 0) what values should go in cells B6:G14 of the following Excel spreadsheet?Free

Essay

Q 64Q 64

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table:
Based on this ILP formulation of the problem what formulas should go in cells F6:F14 of the following Excel spreadsheet?

Free

Essay

Q 65Q 65

A company produces three products which must be painted, assembled, and inspected. The machinery must be cleaned and adjusted before each batch is produced. They want to maximize their profits for the amount of operating time they have. The unit profit and setup cost per batch are:
The operation time per unit and total operating hours available are:
Formulate the ILP for this problem.

Free

Essay

Q 66Q 66

A company produces three products which must be painted, assembled, and inspected. The machinery must be cleaned and adjusted before each batch is produced. They want to maximize their profits for the amount of operating time they have. The unit profit and setup cost per batch are:
The operation time per unit and total operating hours available are:
Based on this ILP formulation of the problem and the optimal solution (X

_{1}, X_{2}, X_{3}) = (270, 0, 0), what values should appear in the shaded cells in the following Excel spreadsheet? X_{i}= amount of product i produced Y_{i}= 1 if product i produced, 0 otherwiseFree

Essay

Q 67Q 67

A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.
The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
Formulate the ILP for this problem capturing the ship choice of ports and the supply-to-demand transportation from the ports to the destinations.

Free

Essay

Q 68Q 68

Exhibit 6.2
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.
The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.2. What formula would go into cell E14?

Free

Short Answer

Q 69Q 69

Exhibit 6.2
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.
The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.2. What formula would go into cells G8:G10?

Free

Essay

Q 70Q 70

Exhibit 6.2
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.
The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
The following is the ILP formulation and a spreadsheet model for the problem.
-Refer to Exhibit 6.2. What formula would go into cells B11:E11 and cells F8:F10?

Free

Essay

Q 71Q 71

The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X

_{1}. Initial solution X_{1}= 4.6X_{2}= 1.6 Obj = 233.9Free

Essay

Q 72Q 72

The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X2.
Initial solution
X

_{1}= 5.0 X_{2}= 7.5 Obj = 550Free

Essay