Question 1

A nonzero reduced gradient value indicates the approximate impact

Accepted Answer

A) on the objective function of very small changes in the value of a given variable 
B) on the RHS of a constraint of a unitary change in the objective function value 
C) on the objective function of very large changes in the value of a given variable 
D) on the objective function of unitary change in the RHS of associated constraint 
A) on the objective function of very small changes in the value of a given variable 
B) on the RHS of a constraint of a unitary change in the objective function value 
C) on the objective function of very large changes in the value of a given variable 
D) on the objective function of unitary change in the RHS of associated constraint

Question 2

A company has collected the following inventory data for an item.What is the total annual cost for this item?
Annual demand for the item D = 500
Unit purchase cost for the item C = 10
Fixed cost of placing an order S = 20
Cost of holding one unit in inventory for a year i = 30%
Order quantity Q = 50

Accepted Answer

A) 275 
B) 450 
C) 5,275 
D) 5,450 
A) 275 
B) 450 
C) 5,275 
D) 5,450

Question 3

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 cell is the objective cell in this problem?
$\begin{array}{|c|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & &  \
\hline2&&\
\hline 3 & \begin{array}{c}
\text { Annual } \
\text { Demand: }
\end{array} &20,000 \
\hline 4 & & \
\hline 5 & \begin{array}{c}
\text { Cost per } \
\text { Unit: }
\end{array} & 25 \% \
\hline 6 & \begin{array}{c}
\text { Ordering } \
\text { Cost: }
\end{array} &\$30 \
\hline 7 & \begin{array}{c}
\text { Carrying } &\
\text { Cost: }
\end{array} &25\% \
\hline 8 & & \
\hline 9 & \text { Order }& 783.73\
& \text { Quantity: } \
\hline 10 &   \
\hline 11 &\text { Total Cost: } &\$ 502,738.61 \
\hline
\end{array}$

Accepted Answer

A) B3 
B) B7 
C) B9 
D) B11 
A) B3 
B) B7 
C) B9 
D) B11

Question 4

The main difference between LP and NLP problems is that NLPs will have a

Accepted Answer

A) linear objective function and nonlinear or linear constraints. 
B) minimum of one nonlinear constraint or a nonlinear objective function. 
C) multilevel objective functions. 
D) multilevel objective function and nonlinear constraints. 
A) linear objective function and nonlinear or linear constraints. 
B) minimum of one nonlinear constraint or a nonlinear objective function. 
C) multilevel objective functions. 
D) multilevel objective function and nonlinear constraints.

Question 5

In a maximization problem,the GRG algorithm's search for a feasible direction of improvement equates to in the simplex algorithm for LP problems.

Accepted Answer

A) an adjacent corner point 
B) a zero reduced cost 
C) a positive shadow price 
D) a positive reduced cost 
A) an adjacent corner point 
B) a zero reduced cost 
C) a positive shadow price 
D) a positive reduced cost

Question 6

In solving the NLP problem,Solver produced a message "Solver cannot improve the current solution.All constraints are satisfied." This means that Solver found:

Accepted Answer

A) a local optimal solution 
B) a global optimal solution 
C) the objective function changed very slowly for the last few iterations 
D) a degenerate model 
A) a local optimal solution 
B) a global optimal solution 
C) the objective function changed very slowly for the last few iterations 
D) a degenerate model

Question 7

The GRG algorithm operates by

Accepted Answer

A) moving in the direction of most rapid improvement in the objective function. 
B) choosing a search direction at random. 
C) searching directly for the optimum solution. 
D) moving in a clockwise direction. 
A) moving in the direction of most rapid improvement in the objective function. 
B) choosing a search direction at random. 
C) searching directly for the optimum solution. 
D) moving in a clockwise direction.

Question 8

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
  
-Refer to Exhibit 8.1.What formula is used in cell D12 of the spreadsheet for this problem?

Accepted Answer

A) =SUMPRODUCTB3:C3,B12:C12) 
B) =SUMPRODUCTB4:C4,B12:C12) 
C) =SUMPRODUCTB5:C5,B12:C12) 
D) =SUMPRODUCTB7:C7,B12:C12) 
A) =SUMPRODUCTB3:C3,B12:C12) 
B) =SUMPRODUCTB4:C4,B12:C12) 
C) =SUMPRODUCTB5:C5,B12:C12) 
D) =SUMPRODUCTB7:C7,B12:C12)

Question 9

The Lagrange Multiplier is similar to which of these terms from linear programming?

Accepted Answer

A) Shadow Price 
B) Allowable Increase 
C) Allowable Decrease 
D) Reduced Cost 
A) Shadow Price 
B) Allowable Increase 
C) Allowable Decrease 
D) Reduced Cost

Question 10

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 ft2 of 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).
Formulate the NLP for the problem.

Accepted Answer

Let L = building length W = building wid

Question 11

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 values would you enter in the Analytic Solver Platform task pane for the above Excel spreadsheet?
Objective Cell: Variables Cells: Constraints Cells:

Accepted Answer

Objective Cell:
D13

Question 12

In solving the NLP problem,Solver produced a message "Solver has converged to the current solution.All constraints are satisfied." This means that:

Accepted Answer

A) Solver found a local optimal solution 
B) Solver found a global optimal solution 
C) the objective function changed very slowly for the last few iterations 
D) Your model is degenerate 
A) Solver found a local optimal solution 
B) Solver found a global optimal solution 
C) the objective function changed very slowly for the last few iterations 
D) Your model is degenerate

Question 13

When using the GRG algorithm to solve NLPs one should try multiple starting points because

Accepted Answer

A) If two different starting points return the same solution,that solution is optimal. 
B) the solution returned depends upon the starting point. 
C) the solution returned is always near the starting point. 
D) a random element of GRG requires multiple starting points. 
A) If two different starting points return the same solution,that solution is optimal. 
B) the solution returned depends upon the starting point. 
C) the solution returned is always near the starting point. 
D) a random element of GRG requires multiple starting points.

Question 14

A company wants to locate a new warehouse to minimize the longest distance travelled by any of its delivery trucks.It has four stores and their coordinates are listed in the below.
 $\begin{array}{rcc}
&\text {X- Coordinate }&\text {Y- Coordinate }\
\hline\text { Store 1 } & 70 & 160 \
\text { Store 2 } & 60 & 90 \
\text { Store 3 } & 180 & 90 \
\text { Store 4 } & 150 & 120
\end{array}$
 
Formulate the NLP for this problem.Let X and Y represent the X,Y coordinates of the new warehouse.

Accepted Answer

^MIN:^Q @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& @#LAT-DLM&

Question 15

The global optimum solution to a nonlinear programming problems NLP),in which the objective function must be maximized,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 16

NLP problems which have slack in all the constraints

Accepted Answer

A) are infeasible. 
B) are only at local optimal solutions. 
C) have zeros for all shadow prices. 
D) are at an interior point of the feasible region. 
A) are infeasible. 
B) are only at local optimal solutions. 
C) have zeros for all shadow prices. 
D) are at an interior point of the feasible region.

Question 17

In NLP a local optimum is best described as

Accepted Answer

A) an interior point. 
B) a corner point. 
C) a point yielding no improving direction. 
D) a good starting point for subsequent searches. 
A) an interior point. 
B) a corner point. 
C) a point yielding no improving direction. 
D) a good starting point for subsequent searches.

Question 18

The main difference between linear LP)and nonlinear programming problems NLP)is that

Accepted Answer

A) NLP may have a nonlinear objective function 
B) All constraints in NLP must be nonlinear 
C) No interaction terms are allowed in NLP 
D) Only one constraint in NLP can be nonlinear 
A) NLP may have a nonlinear objective function 
B) All constraints in NLP must be nonlinear 
C) No interaction terms are allowed in NLP 
D) Only one constraint in NLP can be nonlinear

Question 19

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.What formula goes in cell D4 of the spreadsheet?
$$\begin{array} { | r | c | c | c | r | } 
\hline & \text { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline 1 & & & & \
\hline 2 & & \text { X-Coordinate } & \text { Y-Coordinate } & \
\hline 3 & \text { Warehouse } & 103.800 & 101.000 & \text { Distance: } \
\hline 4 & \text { Store 1 } & 100 & 130 & 70.082 \
\hline 5 & \text { Store 2 } & 90 & 60 & 84.424 \
\hline 6 & \text { Store 3 } & 210 & 80 & 50.749 \
\hline 7 & \text { Store 4 } & 180 & 110 & 18.532 \
\hline 8 & & & & \
\hline 9 & & \text { Total Distance: } &223.787 & \
\hline
\end{array}$$

Accepted Answer

A) =B4-$B$3)^2+C4-$C$3)^2 
B) =SQRTB4-$B$3)+C4-$C$3)) 
C) =SQRTB4-$B$3)^2+C4-$C$3)^2) 
D) =B4-$B$3)+C4-$C$3) 
A) =B4-$B$3)^2+C4-$C$3)^2 
B) =SQRTB4-$B$3)+C4-$C$3)) 
C) =SQRTB4-$B$3)^2+C4-$C$3)^2) 
D) =B4-$B$3)+C4-$C$3)

Question 20

The GRG algorithm terminates when it

Accepted Answer

A) has completed 100 iterations. 
B) has reached the global optimal solution. 
C) when it detects no feasible direction for improvement. 
D) when it reaches the steepest gradient. 
A) has completed 100 iterations. 
B) has reached the global optimal solution. 
C) when it detects no feasible direction for improvement. 
D) when it reaches the steepest gradient.

A nonzero reduced gradient value indicates the approximate impact

A company has collected the following inventory data for an item.What is the total annual cost for this item? Annual demand for the item D = 500 Unit purchase cost for the item C = 10 Fixed cost of placing an order S = 20 Cost of holding one unit in inventory for a year i = 30% Order quantity Q = 50

The main difference between LP and NLP problems is that NLPs will have a

In a maximization problem,the GRG algorithm's search for a feasible direction of improvement equates to in the simplex algorithm for LP problems.

In solving the NLP problem,Solver produced a message "Solver cannot improve the current solution.All constraints are satisfied." This means that Solver found:

The GRG algorithm operates by

The Lagrange Multiplier is similar to which of these terms from linear programming?

In solving the NLP problem,Solver produced a message "Solver has converged to the current solution.All constraints are satisfied." This means that:

When using the GRG algorithm to solve NLPs one should try multiple starting points because

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

NLP problems which have slack in all the constraints

In NLP a local optimum is best described as

The main difference between linear LP)and nonlinear programming problems NLP)is that

The GRG algorithm terminates when it

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

A nonzero reduced gradient value indicates the approximate impact

The main difference between LP and NLP problems is that NLPs will have a

In a maximization problem,the GRG algorithm's search for a feasible direction of improvement equates to in the simplex algorithm for LP problems.

In solving the NLP problem,Solver produced a message "Solver cannot improve the current solution.All constraints are satisfied." This means that Solver found:

The GRG algorithm operates by

The Lagrange Multiplier is similar to which of these terms from linear programming?

In solving the NLP problem,Solver produced a message "Solver has converged to the current solution.All constraints are satisfied." This means that:

When using the GRG algorithm to solve NLPs one should try multiple starting points because

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

NLP problems which have slack in all the constraints

In NLP a local optimum is best described as

The main difference between linear LP)and nonlinear programming problems NLP)is that

The GRG algorithm terminates when it

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