Question 1

In the GRG algorithm the initial solution is called the

Accepted Answer

A) originating point. 
B) insertion point. 
C) zero point. 
D) starting point. 
A) originating point. 
B) insertion point. 
C) zero point. 
D) starting point. D

Question 2

The optimal trade-off between risk and return for a given portfolio problem can be summarized by the

Accepted Answer

A) efficient frontier. 
B) investment frontier. 
C) portfolio boundary. 
D) variance boundary. 
A) efficient frontier. 
B) investment frontier. 
C) portfolio boundary. 
D) variance boundary. A

Question 3

A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of product A costs 25 to make and demand is estimated to be 20 ?
)10 * Price of A.A unit of product B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
$\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20- & 30- & \
& 0.10^{*} \mathrm{P} 1 & 0.07^{*} \mathrm{P}_{2} &
\end{array}$

Let X1 = demand for As and X2 = demand for Bs.Let P1 = price for As and P2 = price for Bs.
The objective function for this problem is?

Accepted Answer

A) $\operatorname { MAX } 25 X _ { 1 } + 18 X _ { 2 }$ 
B) $\left. \left. \operatorname { MAX } 20- 0.1 0 ^ { * } \mathrm { p } _ { 1 } \right) \mathbf { X } _ { 1 } + 3 0- 0.07* \mathrm { p } _ { 2 } \right) \mathbf { X } _ { \mathbf { 2 } }$ 
C) $\operatorname{MAX} 20 P_{1}-0.1 P_{1}^{2}+30 P_{2}-0.07 P_{2}^{2}-1040$ 
D) $\operatorname{MAX} 22.5 P_{1}-0.1 P_{1}^{2}+31.26 P_{2}-0.07 P_{2}^{2}-1040$ 
A) $\operatorname { MAX } 25 X _ { 1 } + 18 X _ { 2 }$ 
B) $\left. \left. \operatorname { MAX } 20- 0.1 0 ^ { * } \mathrm { p } _ { 1 } \right) \mathbf { X } _ { 1 } + 3 0- 0.07* \mathrm { p } _ { 2 } \right) \mathbf { X } _ { \mathbf { 2 } }$ 
C) $\operatorname{MAX} 20 P_{1}-0.1 P_{1}^{2}+30 P_{2}-0.07 P_{2}^{2}-1040$ 
D) $\operatorname{MAX} 22.5 P_{1}-0.1 P_{1}^{2}+31.26 P_{2}-0.07 P_{2}^{2}-1040$ D

Question 4

The total annual cost for the economic order quantity model is

Accepted Answer

A) purchase cost + ordering cost + holding cost. 
B) fixed ordering cost + holding cost. 
C) purchase cost + fixed ordering cost. 
D) unit cost + variable ordering cost + holding cost. 
A) purchase cost + ordering cost + holding cost. 
B) fixed ordering cost + holding cost. 
C) purchase cost + fixed ordering cost. 
D) unit cost + variable ordering cost + holding cost.

Question 5

The GRG and Simplex algorithms are similar in that

Accepted Answer

A) each algorithm process continues until there is no further improvement in the objective function. 
B) both algorithms take their starting solution from the spreadsheet. 
C) both return the globally optimal solution. 
D) both algorithms return a solution that satisfies at least one constraint at equality. 
A) each algorithm process continues until there is no further improvement in the objective function. 
B) both algorithms take their starting solution from the spreadsheet. 
C) both return the globally optimal solution. 
D) both algorithms return a solution that satisfies at least one constraint at equality.

Question 6

The global optimum solution to a nonlinear programming problems NLP),in which the objective function must be minimized,is:

Accepted Answer

A) always larger than the local optimum solution 
B) always smaller than the local optimum solution 
C) is smaller or equal to the local optimum solution 
D) is larger or equal to the local optimum solution 
A) always larger than the local optimum solution 
B) always smaller than the local optimum solution 
C) is smaller or equal to the local optimum solution 
D) is larger or equal to the local optimum solution

Question 7

Which point or points are local optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

Accepted Answer

A) D 
B) E 
C) F 
D) D,F 
A) D 
B) E 
C) F 
D) D,F

Question 8

An office supply company is attempting to determine the order quantity for Mt.White fountain pens which are sold to local executives.Annual demand is 5,000 units and each pen costs the store $50.It costs $75 to place an order and the inventory carrying cost rate is 30% of the value of the item.
Formulate the objective function for this problem.Let Q indicate the order quantity.

Accepted Answer

MIN: 5000

Question 9

What is the straight line Euclidean)distance between the points 5,7)and 1,11)?

Accepted Answer

A) 2.83 
B) 5.65 
C) 8 
D) 16 
A) 2.83 
B) 5.65 
C) 8 
D) 16

Question 10

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &
\end{array}$
 Let XS1U1B11 S1U1B0= demand for As and XS1U1B12 S1U1B0= demand for Bs.Let PS1U1B11 S1U1B0= price for As and PS1U1B12 S1U1B0= price for Bs
  
-An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments.The problem is summarized in the accompanying spreadsheet.The investor has enough money to make an initial investment of $9,000 and hopes he can earn 12%,compounded quarterly,on his investments.He would like to know how low his annual return can be and still allow him to make his payments from interest income.What formula goes in cell C7 of the spreadsheet?

Accepted Answer

A) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4-\mathrm{B} 7$ 
B) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3\right)-\mathrm{B} 7$ 
C) $\left.=\mathrm{B} 7^{*} \$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4-\mathrm{B} 7$ 
D) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4$ 
A) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4-\mathrm{B} 7$ 
B) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3\right)-\mathrm{B} 7$ 
C) $\left.=\mathrm{B} 7^{*} \$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4-\mathrm{B} 7$ 
D) $\left.=\mathrm{B} 7^{*} 1+\$ \mathrm{C} \$ 3 / 4\right)^{\wedge} 4$

Question 11

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &
\end{array}$
 Let XS1U1B11 S1U1B0= demand for As and XS1U1B12 S1U1B0= demand for Bs.Let PS1U1B11 S1U1B0= price for As and PS1U1B12 S1U1B0= price for Bs
  
-An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments.The problem is summarized in the accompanying spreadsheet.The investor has enough money to make an initial investment of $9,000 and hopes he can earn 12%,compounded quarterly,on his investments.He would like to know how low his annual return can be and still allow him to make his payments from interest income.What constraint must be entered in the Risk Solver Platform RSP)task pane?

Accepted Answer

A) $D$7:$D$16 ? $E$7:$E$16 
B) $C$7:$D$16 ? $E$7:$E$16. 
C) $C$7:$C$16 ? $E$7:$E$16 
D) $D$7:$D$16 ? $E$7:$E$16 . 
A) $D$7:$D$16 ? $E$7:$E$16 
B) $C$7:$D$16 ? $E$7:$E$16. 
C) $C$7:$C$16 ? $E$7:$E$16 
D) $D$7:$D$16 ? $E$7:$E$16 .

Question 12

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &
\end{array}$
 Let XS1U1B11 S1U1B0= demand for As and XS1U1B12 S1U1B0= demand for Bs.Let PS1U1B11 S1U1B0= price for As and PS1U1B12 S1U1B0= price for Bs
  
-A company wants to locate a new warehouse to minimize the distance traveled by its delivery trucks.It has four stores and their coordinates are listed in the accompanying spreadsheet.Which cells)in the spreadsheet represent the decision variables in the problem?
$\begin{array}{|r|r|r|r|r|}
\hline & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \
\hline 1 & & & & \
\hline 2 & & \begin{array}{l}
\text { X- } \
\text { Coordinate }
\end{array} & \begin{array}{l}
\text { Y- } \
\text { Coordinate }
\end{array} & \
\hline 3 & \text { Warehouse } & 163.800 & \begin{array}{c}
101.0 \
00
\end{array} & \text { Distance: } \
\hline 4 & \text { Store 1 } & 100 & 130 & 70.082 \
\hline 5 & \text { Store 2 } & 90 & 60 & 84.424 \
\hline 6 & \text { Store 3 } & 210 & 80 & 50.749 \
\hline 7 & \text { Store 4 } & 180 & 110 & 18.532 \
\hline 9 && \text { Total Distance: } & 223.787 & \

\hline
\end{array}$

Accepted Answer

A) B3 
B) B3:C3 
C) B4:C7 
D) D9 
A) B3 
B) B3:C3 
C) B4:C7 
D) D9

Question 13

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &
\end{array}$
 Let XS1U1B11 S1U1B0= demand for As and XS1U1B12 S1U1B0= demand for Bs.Let PS1U1B11 S1U1B0= price for As and PS1U1B12 S1U1B0= price for Bs
  
-An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses.Annual demand is 20,000 units and each cartridge costs the store $25.It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item.The following spreadsheet has been set up to solve the problem.What formula goes in cell B11 in this problem?
$\begin{array}{|c|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & & \
\hline 2 & & \
\hline 3 & \text { Annual Demand: } & 20,000 \
\hline 4 & & \
\hline 5 & \text { Cost per Unit: } & \$ 25 \
\hline 6 & \text { Ordering Cost: } & \$ 30 \
\hline 7 & \text { Carrying Cost: } & 25 \% \
\hline 8 & & \
\hline 9 & \text { Order Quantity: } & 483.73 \
\hline 10 & & \
\hline 11 & \text { Total Cost: } & \$ 502,738.61 \
\hline
\end{array}$

Accepted Answer

A) =B3*B7+B9/B3*B6+B9*2+B5*B7 
B) =B3*B5+B3/B9*B6+B9/2*B5*B7 
C) =SQRTB3*B5+B3/B9*B6+B9/2*B5*B7) 
D) =B3*B3+B3/B9+B6*B9/2*B5*B7 
A) =B3*B7+B9/B3*B6+B9*2+B5*B7 
B) =B3*B5+B3/B9*B6+B9/2*B5*B7 
C) =SQRTB3*B5+B3/B9*B6+B9/2*B5*B7) 
D) =B3*B3+B3/B9+B6*B9/2*B5*B7

Question 14

Which of the following is not an assumption of an EOQ problem.

Accepted Answer

A) Demand for a product is fairly constant. 
B) Inventory depletion rates vary non-linearly. 
C) Each new order is delivered in full when the inventory level reaches 0. 
D) All are valid assumptions. 
A) Demand for a product is fairly constant. 
B) Inventory depletion rates vary non-linearly. 
C) Each new order is delivered in full when the inventory level reaches 0. 
D) All are valid assumptions.

Question 15

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

Accepted Answer

There are three loca

Question 16

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

Accepted Answer

There two local maxi

Question 17

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources,labor and material.The company wants to determine the selling price which will maximize profits.A unit of A costs 25 to make and demand is estimated to be 20 ? .10 * Price of A.A unit of B costs 18 to make and demand is estimated to be 30 ? .07 * Price of B.The utilization of labor and materials and the available quantity of resources is shown in the table.A reasonable price for the products is between 100 and 200.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost\$/unit) } & 25 & 18 & \
\text { Demand units) } & 20-.10^{*} \mathrm{P}_{1} & 30-.07^{*} \mathrm{P}_{2} &
\end{array}$
 Let XS1U1B11 S1U1B0= demand for As and XS1U1B12 S1U1B0= demand for Bs.Let PS1U1B11 S1U1B0= price for As and PS1U1B12 S1U1B0= price for Bs
  
-An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses.Annual demand is 20,000 units and each cartridge costs the store $25.It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item.The following spreadsheet has been set up to solve the problem.What constraint would you impose on this problem to ensure that at least one order is placed per year?
$\begin{array}{|c|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & & \
\hline 2 & & \
\hline 3 & \text { Annual Demand: } & 20,000  \
\hline 4 & & \
\hline 5 & \text { Cost per Unit: } &   \$ 25\
\hline 6 & \text { Ordering Cost: } & \$ 30 \
\hline 7 & \text { Carrying Cost: } & 25 \%\
\hline 8 & &\
\hline 9 & \text { Order Quantity: } & 483.73  \  
\hline 10 & & \
\hline 11 & \text { Total Cost: } &  \$ 502,738.61\
\hline
\end{array}$

Accepted Answer

A) MAX B9 
B) B9 = 1 
C) B9 ? 1 
D) MIN B11 
A) MAX B9 
B) B9 = 1 
C) B9 ? 1 
D) MIN B11

Question 18

Why does the GRG algorithm not provide allowable increase or allowable decrease information with the Reduced Gradient and Lagrange multiplier information?

Accepted Answer

A) Because all constraints have slack. 
B) Because the constraints may not be linear. 
C) Because the solution is not necessarily a global optimum. 
D) Because the solutions are not necessarily corner points. 
A) Because all constraints have slack. 
B) Because the constraints may not be linear. 
C) Because the solution is not necessarily a global optimum. 
D) Because the solutions are not necessarily corner points.

Question 19

An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments.The problem is summarized in the accompanying spreadsheet.The investor has enough money to make an initial investment of $12,000 and hopes he can earn 18% on his investments.He would like to know how low his annual return can be and still allow him to make his payments from interest income.
If the Analytic Solver Platform is used,which are the Objective,Variables and Constraint cells in the spreadsheet for this problem?

Accepted Answer

Objective: C3
Variab

Question 20

Exhibit 8.2
The following questions pertain to the problem and spreadsheet below.
A construction company just purchased a 300 × 300 foot lot upon which they plan to build an office building.They need at least 60,000 ftS1U1P12 S1S1P0of office floor space.Zoning regulations require each floor be 10 feet high and the building not exceed 65 ft in height.Further,parking space must equal at least 30% of the total floor space available.The company's cost accountant uses a 60% factor of the building height and a 1% factor of any story's floor area to calculate the total building cost in millions of dollars).
The following is the NLP formulation for the problem.
   The spreadsheet implementation of this formulation applies to the following questions.
  
-Refer to Exhibit 8.2.What formula would you place into cell B5 to calculate Total Floor Area?

Accepted Answer

The answer of Exhibit 8.2
The following questions pertain to the...

In the GRG algorithm the initial solution is called the

The optimal trade-off between risk and return for a given portfolio problem can be summarized by the

The total annual cost for the economic order quantity model is

The GRG and Simplex algorithms are similar in that

The global optimum solution to a nonlinear programming problems NLP),in which the objective function must be minimized,is:

Which point or points are local optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

What is the straight line Euclidean)distance between the points 5,7)and 1,11)?

Which of the following is not an assumption of an EOQ problem.

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

Why does the GRG algorithm not provide allowable increase or allowable decrease information with the Reduced Gradient and Lagrange multiplier information?

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

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 8: Nonlinear Programming and Evolutionary Optimization

In the GRG algorithm the initial solution is called the

The optimal trade-off between risk and return for a given portfolio problem can be summarized by the

The total annual cost for the economic order quantity model is

The GRG and Simplex algorithms are similar in that

The global optimum solution to a nonlinear programming problems NLP),in which the objective function must be minimized,is:

Which point or points are local optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

What is the straight line Euclidean)distance between the points 5,7)and 1,11)?

Which of the following is not an assumption of an EOQ problem.

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

Why does the GRG algorithm not provide allowable increase or allowable decrease information with the Reduced Gradient and Lagrange multiplier information?

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

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters