Question 1

Variables, which are not required to assume strictly integer values are referred to as

Accepted Answer

A)  strictly non-integer. 
B)  continuous. 
C)  discrete. 
D)  infinite. 
A)  strictly non-integer. 
B)  continuous. 
C)  discrete. 
D)  infinite.

Question 2

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.
 $$\begin{array} { c c c c c } 
& { \text { Destination } } \
\mathrm { Port } & \mathrm { D } 1 & \mathrm { D } 2 & \mathrm { D } 3 & \mathrm { D } 4 \
\hline \mathrm { A } & 75 & 88 & 103 & 56 \
\mathrm {~B} & 105 & 76 & 101 & 85 \
\mathrm { C } & 43 & 80 & 95 & 62 \
\hline \text { Demand } & 500 & 600 & 450 & 700
\end{array}$$
 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.
 $ Y_{i j} $ be 1 if ship 1 travels to port $ j $, for $ 1=S 1, S 2 $ and $ j=A, B, C $ $ \mathrm{X}_{\mathbf{k}} $ be the tons shipped from poit $ j=A, B, C $ to Destination $ k=D 1, D 2, D 3 $, D4

$\begin{array}{ll}
\text { Minimize } & 75 \mathrm{X}_{11}+88 \mathrm{X}_{12}+103 \mathrm{X}_{13}+56 \mathrm{X}_{14}+105 \mathrm{X}_{21}+76 \mathrm{X}_{22}+101 \mathrm{X}_{23}+85 \mathrm{X}_{24}+43 \mathrm{X}_{31} \
& +80 \mathrm{X}_{32}+95 \mathrm{X}_{33}+62 \mathrm{X}_{34}
\end{array}$

Subject to:
$
\begin{array}{l}
\mathrm{Y}_{11}+\mathrm{Y}_{21} \leq 1 \
\mathrm{Y}_{12}+\mathrm{Y}_{22} \leq 1 \
\mathrm{Y}_{13}+\mathrm{Y}_{23} \leq 1 \
\mathrm{Y}_{11}+\mathrm{Y}_{12}+\mathrm{Y}_{13}=1 \
\mathrm{Y}_{21}+\mathrm{Y}_{22}+\mathrm{Y}_{23}=1 \
\mathrm{X}_{14}+\mathrm{X}_{15}+\mathrm{X}_{16}+\mathrm{X}_{17} \leq 1200 \mathrm{Y}_{11}+1120 \mathrm{Y}_{21} \
\mathrm{X}_{24}+\mathrm{X}_{25}+\mathrm{X}_{26}+\mathrm{X}_{27} \leq 1200 \mathrm{Y}_{12}+1120 \mathrm{Y}_{22} \
\mathrm{X}_{34}+\mathrm{X}_{35}+\mathrm{X}_{36}+\mathrm{X}_{37} \leq 1200 \mathrm{Y}_{13}+1120 \mathrm{Y}_{23} \
\mathrm{X}_{14}+\mathrm{X}_{24}+\mathrm{X}_{34} \geq 500 \
\mathrm{X}_{15}+\mathrm{X}_{25}+\mathrm{X}_{35} \geq 600 \
\mathrm{X}_{16}+\mathrm{X}_{26}+\mathrm{X}_{36} \geq 450 \
\mathrm{X}_{17}+\mathrm{X}_{27}+\mathrm{X}_{37} \geq 700 \
\mathrm{Y}_{\mathrm{ij}} \mathrm{X}_{\mathrm{i}} \geq 0
\end{array}
$

-Refer to Exhibit 6.2. What formula would go into cells G8:G10?

Accepted Answer

The answer of Exhibit 6.2
The following questions pertain to the...

Question 3

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3?

Accepted Answer

A)  X31$\le$M3Y3, X32 $\ge$50Y3 
B)  X31 $\le$ M3Y3, X31 $\ge$ 50 
C)  X32 $\ge$ (1/50)X31, X31 $\le$ 50 
D)  X32 $\le$ M3Y3, X31 $\ge$50Y3 
A)  X31$\le$M3Y3, X32 $\ge$50Y3 
B)  X31 $\le$ M3Y3, X31 $\ge$ 50 
C)  X32 $\ge$ (1/50)X31, X31 $\le$ 50 
D)  X32 $\le$ M3Y3, X31 $\ge$50Y3

Question 4

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.
 $\begin{array}{ll}
\text { MAX: } & 50 \mathrm{X}_{1}+40 \mathrm{X}_{2} \
\text { Subject to: } & 2 \mathrm{X}_{1}+4 \mathrm{X}_{2} \leq 40 \
& 3 \mathrm{X}_{1}+2 \mathrm{X}_{2} \leq 30 \
& \mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \text { and integer }
\end{array}$
 Initial solution
X1 = 5.0
X2 = 7.5
Obj = 550

Accepted Answer

Question 5

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.
 $$\begin{array} { c l c c } 
\text { Variable } & \text { Decision } & \begin{array} { c } 
\text { NPV } \
(\text  {\$ million } ) 
\end{array} & \begin{array} { c } 
\text { Cost } \
\text  {\$ million } )
\end{array} \
\hline \mathbf { X } _ { 1 } & \text { Factory in Columbia } & 3 & 10 \
\mathbf { X } _ { \mathbf { 2 } } & \text { Factory in Atlanta } & 4 & 8 \
\mathbf { X } _ { 3 } & \text { Warehouse in Columbia } & 2 & 0 \
\mathbf { X } _ { 4 } & \text { Warehouse in Atlanta } & 1 & 5
\end{array}$$ 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?
 $\mathrm { MAX } : \quad 3 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } + 2 \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 }$
Subject to:
$$
\begin{array}{l}
3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+2 \mathrm{X}_{3}+\mathrm{X}_{4} \
10 \mathrm{X}_{1}+8 \mathrm{X}_{2}+6 \mathrm{X}_{3}+5 \mathrm{X}_{4} \leq 15 \
\mathrm{X}_{1}+\mathrm{X}_{2}=1 \
\mathrm{X}_{3}+\mathrm{X}_{4} \leq 1 \
\mathrm{X}_{3}-\mathrm{X}_{1} \leq 0 \
\mathrm{X}_{4}-\mathrm{X}_{2} \leq 0 \
\mathrm{X}_{\mathrm{i}}=0,1
\end{array}
$$
Solution: $ \left(\mathrm{X}_{1}, \mathrm{X}_{2} \mathrm{X}_{3}, \mathrm{X}_{4}\right)=(0,1,0,1 )$

Accepted Answer

The answer of A company wants to build a new...

Question 6

A company is planning next month's production. It has to pay a setup cost to produce a batch of X4'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 Y4 and the production quantity variable X4?

Accepted Answer

A)  X4 $\le$M4Y4, X4 $\ge$ 100 
B)  X4 $\le$M4Y4, X4 = 100 Y4 
C)  X4 $\le$ M4Y4, X4 $\ge$100 Y4 
D)  X4 $\le$M4Y4, X4 $\le$ 100 Y4 
A)  X4 $\le$M4Y4, X4 $\ge$ 100 
B)  X4 $\le$M4Y4, X4 = 100 Y4 
C)  X4 $\le$ M4Y4, X4 $\ge$100 Y4 
D)  X4 $\le$M4Y4, X4 $\le$ 100 Y4

Question 7

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?

Accepted Answer

A)  X1 + X2 + X3 + X4 = 1 
B)  X1 + X2 + X3 + X4 $\le$1 
C)  X1 + X2 + X3 + X4 $\ge$ 1 
D)  X1 + X2 + X3 + X4 $\ge$ 0 
A)  X1 + X2 + X3 + X4 = 1 
B)  X1 + X2 + X3 + X4 $\le$1 
C)  X1 + X2 + X3 + X4 $\ge$ 1 
D)  X1 + X2 + X3 + X4 $\ge$ 0

Question 8

Which of the following are potential pitfalls of using a non-zero integer tolerance factor in the Risk Solver Platform (RSP)?

Accepted Answer

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. 
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.

Question 9

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:
 $\begin{array}{ccc}
\text { Product } & \text { Profit per unit } & \text { Setup cost per batch } \
\hline 1 & 9 & 500 \
2 & 10 & 600 \
3 & 10 & 650
\end{array}$
 The operation time per unit and total operating hours available are:
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text {Operating Time per Unit}}$$\quad $$\quad $$\quad $$\quad $$\quad $$\text {Operating}$
$\begin{array}{lcccc}
\text { Operation } & \text { Product 1 } & \text { Product 2 } & \text { Product 3 } & \text { Hours Available } \
\hline \text { Paint } & 1 & 2 & 2 & 400 \
\text { Assemble } & 2 & 3 & 2 & 600 \
\text { Inspection } & 2 & 4 & 3 & 540
\end{array}$

Based on this ILP formulation of the problem and the optimal solution (X1, X2, X3) = (270, 0, 0), what values should appear in the shaded cells in the following Excel spreadsheet?
Xi = amount of product i produced
Yi = 1 if product i produced, 0 otherwise
 MAX: $\quad 9 X _ { 1 } + 10 X _ { 2 } + 12 X _ { 3 } - 500 Y _ { 1 } - 600 Y _ { 2 } - 650 Y _ { 3 }$
Subject to:
$
\begin{array}{l}
1 \mathrm{X}_{1}+2 \mathrm{X}_{2}+2 \mathrm{X}_{3} \leq 400 \
2 \mathrm{X}_{1}+3 \mathrm{X}_{2}+2 \mathrm{X}_{3} \leq 600 \
2 \mathrm{X}_{1}+4 \mathrm{X}_{2}+3 \mathrm{X}_{3} \leq 540 \
\mathrm{X}_{1} \leq \mathrm{M}_{1} \mathrm{Y}_{1} \text { OR } 270 \mathrm{Y}_{1} \
\mathrm{X}_{2} \leq \mathrm{M}_{2} \mathrm{Y}_{2} \text { OR } 135 \mathrm{Y}_{2} \
\mathrm{X}_{3} \leq \mathrm{M}_{3} \mathrm{Y}_{3} \mathrm{OR} 180 \mathrm{Y}_{3} \
\mathrm{Y}_{\mathrm{i}}=0,1 \
\mathrm{X}_{\mathrm{i}} \geq 0 \text { and integer }
\end{array}
$

Accepted Answer

Question 10

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:
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text { Tower Sites }}$
$\begin{array}{ccccc}
\text { Region } & 1 & 2 & 3 & 4 \
\hline \text { A } & & 1 & & 1 \
\text { B } & 1 & & 1 & 1 \
\text { C } & 1 & 1 & 1 & \
\text { D } & 1 & & & 1 \
\hline \text { COST }(\$ 000 \mathrm{~s}) & 200 & 150 & 190 & 250
\end{array}$

$\text { MIN: } \quad 200 \mathrm{X}_{1}+150 \mathrm{X}_{2}+190 \mathrm{X}_{3}+250 \mathrm{X}_{4}$

$\text { Subject to:}$
$
\begin{array}{l}
\mathrm{X}_{2}+\mathrm{X}_{4} \geq 1 \
\mathrm{X}_{1}+\mathrm{X}_{3}+\mathrm{X}_{4} \geq 1 \
\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3} \geq 1 \
\mathrm{X}_{1}+\mathrm{X}_{4} \geq 1 \
\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}=2 \
\mathrm{X}_{\mathrm{i}}=0,1
\end{array}
$ Based on this ILP formulation of the problem what formulas should go in cells F6:F14 of the following Excel spreadsheet?

Accepted Answer

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

Question 11

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.
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text { Project Funds Required (in $ \$ 000 $ )}}$$\quad $$\quad $$\quad $$\text { Benefit}$
$\begin{array}{cccccccc}
\text { Project } & 1 & 2 & 3 & 4 & 5 & \text { (in } \$ 000 \text { s) } \
\hline 1 & \$  70 & \$ 40 & \$ 30 & \$ 15 & \$ 15 & \$ 160 \
2 & \$ 82 & \$ 35 & \$ 20 & \$ 20 & \$ 10 & \$ 190 \
3 & \$  55 & \$ 10 & \$ 10 & \$ 5 & & \$ 125 \
4 & \$  69 & \$ 17 & \$ 15 & \$ 12 & \$ 8 & \$ 139 \
5 & \$  75 & \$ 20 & \$ 25 & \$ 30 & \$ 45 & \$ 174\
\text { Budget } & \$ 225 \mathrm{~K} &\$ 60 \mathrm{~K} & \$ 60 \mathrm{~K} & \$ 50 \mathrm{~K} &\$ 50 \mathrm{~K} 
\end{array}$
 Define the ILP formulation for this capital budgeting problem.

Accepted Answer

The answer of A research director must pick a subset...

Question 12

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.

Accepted Answer

Let X_i = 0 if project

Question 13

How is an LP problem changed into an ILP problem?

Accepted Answer

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. 
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.

Question 14

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. $\quad $$\quad $$\quad $$\quad $$\text { Hours required by }$
$\begin{array}{lccc}
\text { Operation } & \text { A } & \text { B } & \text { Hours } \
\hline \text { Cutting } & 3 & 4 & 48 \
\text { Welding } & 2 & 1 & 36
\end{array}$
 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$12/B12)*B14 
A)  =B5- MIN($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 15

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.
 $$\begin{array} { c c c c c } 
& { \text { Destination } } \
\mathrm { Port } & \mathrm { D } 1 & \mathrm { D } 2 & \mathrm { D } 3 & \mathrm { D } 4 \
\hline \mathrm { A } & 75 & 88 & 103 & 56 \
\mathrm {~B} & 105 & 76 & 101 & 85 \
\mathrm { C } & 43 & 80 & 95 & 62 \
\hline \text { Demand } & 500 & 600 & 450 & 700
\end{array}$$ 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.

Accepted Answer

The answer of A certain military deployment requires supplies delivered...

Question 16

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:
 $$\begin{array} { l c c l r } 
\text { Days af Week } & \text { Workers Requirad } & \text { Shift } & \text { Days off } & \text { Wage } \
\hline \text { Sunday } & 54 & 1 & \text { Sun \& Man } & 900 \
\text { Monday } & 50 & 2 & \text { Man \& Tue } & 1000 \
\text { Tuesday } & 36 & 3 & \text { Tue \&Wed } & 1000 \
\text { Wednesday } & 38 & 4 & \text { Wed\&Thur } & 1000 \
\text { Thursday } & 42 & 5 & \text { Thur \& Fri } & 1000 \
\text { Friday } & 40 & 6 & \text { Fri \& Sat } & 900 \
\text { Saturday } & 48 & 7 & \text { Sat \& Sun } & 850
\end{array}$$ $\text { MIN: } \quad 900 \mathrm{X}_{1}+1000 \mathrm{X}_{2}+1000 \mathrm{X}_{3}+1000 \mathrm{X}_{4}+1000 \mathrm{X}_{5}+900 \mathrm{X}_{6}+850 \mathrm{X}_{7}$

$\text { Subject to:}$
$
\begin{array}{l}
\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6} \geq 54 \
\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7} \geq 50 \
\mathrm{X}_{4}+\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1} \geq 36 \
\mathrm{X}_{5}+\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2} \geq 38 \
\mathrm{X}_{6}+\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3} \geq 42 \
\mathrm{X}_{7}+\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4} \geq 40 \
\mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}+\mathrm{X}_{5} \geq 48 \
\mathrm{X}_{\mathrm{i}} \geq 0 \text { and integer }
\end{array}
$

Based on this ILP formulation of the problem and the optimal solution (X1, X2, X3, X4, X5, X6) = (2, 10, 16, 6, 14, 8, 6) what values should go in cells B5:J13 of the following Excel spreadsheet?

Accepted Answer

Question 17

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:
 $$\begin{array} { l c c l r } 
\text { Days af Week } & \text { Warkers Requirad } & \text { Shift } & \text { Days off } & \text { Wage } \
\hline \text { Sunday } & 54 & 1 & \text { Sun \& Man } & 900 \
\text { Monday } & 50 & 2 & \text { Man\& Tue } & 1000 \
\text { Tuesday } & 36 & 3 & \text { Tue \&Wed } & 1000 \
\text { Wednesday } & 38 & 4 & \text { Wed \& Thur } & 1000 \
\text { Thursday } & 42 & 5 & \text { Thur \& Fri } & 1000 \
\text { Friday } & 40 & 6 & \text { Fri \& Sat } & 900 \
\text { Saturday } & 48 & 7 & \text { Sat \& Sun } & 850
\end{array}$$ Formulate the ILP for this problem.

Accepted Answer

The answer of A company needs to hire workers to...

Question 18

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. 
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 19

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?

Accepted Answer

A)  X1 $\ge$ M2Y2 
B)  X1$\le$M2X2 
C)  X1$\le$M1Y1, X1 $\le$Y1X2 
D)  X1 $\le$X2 
A)  X1 $\ge$ M2Y2 
B)  X1$\le$M2X2 
C)  X1$\le$M1Y1, X1 $\le$Y1X2 
D)  X1 $\le$X2

Question 20

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.
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text { To zone }}$
$\begin{array}{l}
\begin{array} { c c c c c c } 
 \text { No. tall building } & \text { From zone } & 1 & 2 & 3 & 4 \
\hline 50 & 1 & 0 & 2 & 1 & 6 \
90 & 2 & 2 & 0 & 4 & 5 \
60 & 3 & 1 & 4 & 0 & 1 \
70 & 4 & 6 & 5 & 1 & 0
\end{array}
\end{array}$
 Based on this ILP formulation of the problem what values should go in cells B5:G24 of the following Excel spreadsheet?
Let Xi = 1 if truck located in zone i, 0 otherwise
 $$\begin{array} { c l c } 
\text { Zone } & \text { Covers these zones } & \text { With this many buldings} \
\hline 1 & 1,2,3 & 200 \
2 & 1,2 & 140 \
3 & 1,3,4 & 180 \
4 & 3,4 & 130
\end{array}$$ $\text { MAX: } \quad 200 \mathrm{X}_{1+}+140 \mathrm{X}_{2}+180 \mathrm{X}_{3}+130 \mathrm{X}_{4}$

$\begin{array}{ll}
\text { Subject to: } & \mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}=2 \
& \mathrm{X}_{1}+\mathrm{X}_{2} \leq 1 \
& \mathrm{X}_{\mathrm{i}}=0,1
\end{array}$

Accepted Answer

Variables, which are not required to assume strictly integer values are referred to as

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?

Which of the following are potential pitfalls of using a non-zero integer tolerance factor in the Risk Solver Platform (RSP)?

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.

How is an LP problem changed into an ILP problem?

The objective function value for the ILP problem can never

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?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 6: Integer Linear Programming

Variables, which are not required to assume strictly integer values are referred to as

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?

Which of the following are potential pitfalls of using a non-zero integer tolerance factor in the Risk Solver Platform (RSP)?

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.

How is an LP problem changed into an ILP problem?

The objective function value for the ILP problem can never

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?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters