Question 1

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?  ​

Accepted Answer

The answer of An investor has $500,000 to invest and...

Question 2

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 (X₁, X₂, X₃, X₄) = (1, 1, 0, 0) what values should go in cells B6:G14 of the following Excel spreadsheet?

Accepted Answer

The answer of A cellular phone company wants to locate...

Question 3

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 X₁ = 5.0 X₂ = 7.5 Obj = 550

Accepted Answer

The answer of The following ILP is being solved by...

Question 4

The concept of an upper bound in IP is associated with:

Accepted Answer

A)  LP relaxation of a minimization problem 
B)  LP relaxation of a maximization problem 
C)  a cutting plane technique 
D)  explicit enumeration of corner point solutions

Question 5

An ILP problem has 5 binary decision variables. How many possible integer solutions are there to this problem?

Accepted Answer

A)  5 
B)  10 
C)  25 
D)  32

Question 6

Pure IP formulation requires that:

Accepted Answer

A)  all decision variables must be integer 
B)  the optimal objective function value must be integer 
C)  some decision variables must be integer 
D)  some decision variables and the optimal value of the objective function must be integer

Question 7

What does the Analytic Solver Platform integer tolerance factor of 0 accomplish?

Accepted Answer

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.

Question 8

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
Xi = the amount of product i produced
Yi = 1 if Xi > 0 and 0 if Xi = 0
Using the approach discussed in the text, what is the appropriate value for M1 in the linking constraint for product A?

Accepted Answer

A)  2 
B)  3 
C)  16 
D)  12

Question 9

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?

Accepted Answer

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)

Question 10

Suppose you want to minimize an objective function z=2x1+3x2. Both decision variables must be integer. The optimal solution to the LP relaxation will:

Accepted Answer

A)  be smaller than the optimal IP solution 
B)  be larger than the optimal IP solution 
C)  can be either smaller or larger than the optimal IP solution 
D)  will be within 5% of the optimal IP solution value

Question 11

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?

Accepted Answer

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

Question 12

In the B & B algorithm, B & B stands for

Accepted Answer

A)  Brooks and Baker 
B)  Best Bound 
C)  Best Branch 
D)  Branch and Bound

Question 13

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

Accepted Answer

A)  decision variables. 
B)  production cost constraint coefficients. 
C)  variable costs. 
D)  marginal costs.

Question 14

The objective function value for the ILP problem can never

Accepted Answer

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.

Question 15

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.  ​

Accepted Answer

The answer of A city wants to locate 2 new...

Question 16

Binary variables are useful for modeling

Accepted Answer

A)  the fixed-charge problem 
B)  the assignment problem 
C)  the transportation problem 
D)  the shortest route problem

Question 17

A practical way of dealing with the complexity of IP problems is to:

Accepted Answer

A)  stop searching for a better solution when the current best solution is within specified suboptimality tolerances 
B)  continue searching for the optimal solution until no further objective function improvement can be achieved 
C)  use a B&B technique 
D)  use LP relaxation and round the values of the decision variables to the nearest integers

Question 18

An integrality condition indicates that some (or all) of the

Accepted Answer

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

Question 19

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?

Accepted Answer

The answer of Exhibit 6.1
The following questions pertain to the...

Question 20

How is the integer tolerance factor set in the Analytic Solver Platform (ASP)?

Accepted Answer

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 ASP Options dialog box. 
C)  By choosing the 100% Precision field in the ASP Options dialog box. 
D)  By entering the desired tolerance factor value in the Integer Tolerance field of ASP.

Exam 6: Integer Linear Programming

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 X₁ = 5.0 X₂ = 7.5 Obj = 550

The concept of an upper bound in IP is associated with:

An ILP problem has 5 binary decision variables. How many possible integer solutions are there to this problem?

Pure IP formulation requires that:

What does the Analytic Solver Platform integer tolerance factor of 0 accomplish?

Suppose you want to minimize an objective function z=2x₁+3x₂. Both decision variables must be integer. The optimal solution to the LP relaxation will:

In the B & B algorithm, B & B stands for

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

The objective function value for the ILP problem can never

Binary variables are useful for modeling

A practical way of dealing with the complexity of IP problems is to:

An integrality condition indicates that some (or all) of the

How is the integer tolerance factor set in the Analytic Solver Platform (ASP) ?

Exam 6: Integer Linear Programming

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 X1 = 5.0 X2 = 7.5 Obj = 550

The concept of an upper bound in IP is associated with:

An ILP problem has 5 binary decision variables. How many possible integer solutions are there to this problem?

Pure IP formulation requires that:

What does the Analytic Solver Platform integer tolerance factor of 0 accomplish?

Suppose you want to minimize an objective function z=2x1+3x2. Both decision variables must be integer. The optimal solution to the LP relaxation will:

In the B & B algorithm, B & B stands for

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

The objective function value for the ILP problem can never

Binary variables are useful for modeling

A practical way of dealing with the complexity of IP problems is to:

An integrality condition indicates that some (or all) of the

How is the integer tolerance factor set in the Analytic Solver Platform (ASP) ?

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 X₁ = 5.0 X₂ = 7.5 Obj = 550

Suppose you want to minimize an objective function z=2x₁+3x₂. Both decision variables must be integer. The optimal solution to the LP relaxation will: