Question 1

If a problem has infinite number solutions,the objective function

Accepted Answer

A) is parallel to one of the binding constraints. 
B) goes through exactly one corner point of the feasible region. 
C) cannot identify a feasible region. 
D) is infeasible. 
A) is parallel to one of the binding constraints. 
B) goes through exactly one corner point of the feasible region. 
C) cannot identify a feasible region. 
D) is infeasible.

Question 2

The following linear programming problem has been written to plan the production of two products.The company wants to maximize its profits.
X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch
MAX: 150 X1 + 250 X2
Subject to: 2 X1 + 5 X2 ≤ 200 − resource 1
3 X1 + 7 X2 ≤ 175 − resource 2 X1,X2 ≥ 0
How many units of resource 1 are consumed by each unit of product 1 produced?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 5 
A) 1 
B) 2 
C) 3 
D) 5

Question 3

A diet is being developed which must contain at least 100 mg of vitamin C.Two fruits are used in this diet.Bananas contain 30 mg of vitamin C and Apples contain 20 mg of vitamin C.The diet must contain at least 100 mg of vitamin C Which of the following constraints reflects the relationship between Bananas,Apples and vitamin C?

Accepted Answer

A) 20 A + 30 B ≥ 100 
B) 20 A + 30 B ≤ 100 
C) 20 A + 30 B = 100 
D) 20 A = 100 
A) 20 A + 30 B ≥ 100 
B) 20 A + 30 B ≤ 100 
C) 20 A + 30 B = 100 
D) 20 A = 100

Question 4

The second step in formulating a linear programming problem is

Accepted Answer

A) Identify any upper or lower bounds on the decision variables. 
B) State the constraints as linear combinations of the decision variables. 
C) Understand the problem. 
D) Identify the decision variables. 
E) State the objective function as a linear combination of the decision variables. 
A) Identify any upper or lower bounds on the decision variables. 
B) State the constraints as linear combinations of the decision variables. 
C) Understand the problem. 
D) Identify the decision variables. 
E) State the objective function as a linear combination of the decision variables.

Question 5

The Byte computer company produces two models of computers,Plain and Fancy.It wants to plan how many computers to produce next month to maximize profits.Producing these computers requires wiring,assembly and inspection time.Each computer produces a certain level of profits but faces a limited demand.There are a limited number of wiring,assembly and inspection hours available next month.The data for this problem is summarized in the following table.
 $$\begin{array} { l c c c c c } 
& & \text { Mazamum } & \text { Assembly } & \text { Inspectio } \
\text { Computer } & \text { Profit per } & \text { demand for } & \text { Wiring Hours } & \text { Hours } & \text { n } \
 \text { Model }  & \text { Madel } 5 \text { ) } & \text { product } & \text { Required } & \text { Required } & \text { Haurs } \
\hline \text { Plain } & 30 & 80 & 0.4 & 0.5 & 0.2 \
\text { Fancy } & 40 & 90 & 0.5 & 0.4 & 0.3 \
\hline & & \text { Hour5 Ayailable } & 50 & 50 & 22
\end{array}$$ 
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.

Accepted Answer

a.Let XS1U1B11 S1U1B0= Number of Plain computers produ

Question 6

This graph shows the feasible region defined by points ACDEF)and objective function level curve BG)for a maximization problem.Which point corresponds to the optimal solution to the problem?

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E

Question 7

The following diagram shows the constraints for a LP model.Assume the point 0,0)satisfies constraint B,J)but does not satisfy constraints D,H)or C,I).Which set of points on this diagram defines the feasible solution space?

Accepted Answer

A) A,B,E,F,H 
B) A,D,G,J 
C) F,G,H,J 
D) F,G,I,J 
A) A,B,E,F,H 
B) A,D,G,J 
C) F,G,H,J 
D) F,G,I,J

Question 8

A facility produces two products.The labor constraint in hours)is formulated as: 350x1+300x2 ≤ 10,000.The
Number 10,000 represents

Accepted Answer

A) a profit contribution of one unit of product 1. 
B) one unit of product 1 uses 10,000 hours of labor. 
C) there are 10,000 hours of labor available for use. 
D) the problem has no objective function. 
A) a profit contribution of one unit of product 1. 
B) one unit of product 1 uses 10,000 hours of labor. 
C) there are 10,000 hours of labor available for use. 
D) the problem has no objective function.

Question 9

When do alternate optimal solutions occur in LP models?

Accepted Answer

A) When a binding constraint is parallel to a level curve. 
B) When a non-binding constraint is perpendicular to a level curve. 
C) When a constraint is parallel to another constraint. 
D) Alternate optimal solutions indicate an infeasible condition. 
A) When a binding constraint is parallel to a level curve. 
B) When a non-binding constraint is perpendicular to a level curve. 
C) When a constraint is parallel to another constraint. 
D) Alternate optimal solutions indicate an infeasible condition.

Question 10

A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced.Which of the following constraints reflects this fact?

Accepted Answer

A) fX1,X2,X3,X4)≤ b1 
B) fX1,X2,X3,X4)≥ b1 
C) fX1,X2,X3,X4)= b1 
D) fX1,X2,X3,X4)≠ b1 
A) fX1,X2,X3,X4)≤ b1 
B) fX1,X2,X3,X4)≥ b1 
C) fX1,X2,X3,X4)= b1 
D) fX1,X2,X3,X4)≠ b1

Question 11

Level curves are used when solving LP models using the graphical method.To what part of the model do level curves relate?

Accepted Answer

A) constraints 
B) boundaries 
C) right hand sides 
D) objective function 
A) constraints 
B) boundaries 
C) right hand sides 
D) objective function

Question 12

Which of the following actions would expand the feasible region of an LP model?

Accepted Answer

A) Loosening the constraints. 
B) Tightening the constraints. 
C) Multiplying each constraint by 2. 
D) Adding an additional constraint. 
A) Loosening the constraints. 
B) Tightening the constraints. 
C) Multiplying each constraint by 2. 
D) Adding an additional constraint.

Question 13

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Accepted Answer

A) infeasible. 
B) open ended. 
C) multi-optimal. 
D) unbounded. 
A) infeasible. 
B) open ended. 
C) multi-optimal. 
D) unbounded.

Question 14

The objective function for a LP model is 3 X1 + 2 X2.If X1 = 20 and X2 = 30,what is the value of the objective function?

Accepted Answer

A) 0 
B) 50 
C) 60 
D) 120 
A) 0 
B) 50 
C) 60 
D) 120

Question 15

The following linear programming problem has been written to plan the production of two products.The company wants to maximize its profits.
X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch
MAX: 150 X1 + 250 X2
Subject to: 2 X1 + 5 X2 ≤ 200
3 X1 + 7 X2 ≤ 175 X1,X2 ≥ 0
How many units of resource two the second constraint)are unutilized if the company produces 10 units of product 1 and 5 units of product 2?

Accepted Answer

A) 110 
B) 150 
C) 155 
D) 100 
A) 110 
B) 150 
C) 155 
D) 100

Question 16

A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2.There are only 150 pounds of resource 1 available.Which of the following constraints reflects the relationship between X1,X2 and resource 1?

Accepted Answer

A) 4 X1 + 3 X2 ≥ 150 
B) 4 X1 + 3 X2 ≤ 150 
C) 4 X1 + 3 X2 = 150 
D) 4 X1 ≤ 150 
A) 4 X1 + 3 X2 ≥ 150 
B) 4 X1 + 3 X2 ≤ 150 
C) 4 X1 + 3 X2 = 150 
D) 4 X1 ≤ 150

Question 17

The first step in formulating a linear programming problem is

Accepted Answer

A) Identify any upper or lower bounds on the decision variables. 
B) State the constraints as linear combinations of the decision variables. 
C) Understand the problem. 
D) Identify the decision variables. 
E) State the objective function as a linear combination of the decision variables. 
A) Identify any upper or lower bounds on the decision variables. 
B) State the constraints as linear combinations of the decision variables. 
C) Understand the problem. 
D) Identify the decision variables. 
E) State the objective function as a linear combination of the decision variables.

Question 18

The constraint for resource 1 is 5 X1 + 4 X2 ≤ 200.If X1 = 20 and X2 = 5,how much of resource 1 is unused?

Accepted Answer

A) 0 
B) 80 
C) 100 
D) 200 
A) 0 
B) 80 
C) 100 
D) 200

Question 19

Project 2.1
Joey Koons runs a small custom computer parts company.As a sideline he offers customized and pre-built computer system packages.In preparation for the upcoming school year,he has decided to offer two custom computer packages tailored for what he believes are current student needs.System A provides a strong computing capability at a reasonable cost while System B provides a much more powerful computing capability,but at a higher cost.Joey has a fairly robust parts inventory but is concerned about his stock of those components that are common to each proposed system.A portion of his inventory,the item cost,and inventory level is provided in the table below.
 \(\begin{array}{llclclclc}
\text { Part } & \begin{array}{l}
\text { Type/ } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { On } \
\text { Hand }
\end{array} & \begin{array}{l}
\text { Type/ } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { On } \
\text { Hand }
\end{array} & \begin{array}{l}
\text { Type/ } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { On } \
\text { Hand }
\end{array} & \begin{array}{l}
\text { Type/ } \
\text { Cost }
\end{array} & \begin{array}{c}
\text { Ond } \
\text { Hand }
\end{array} \
\hline \text { Processo } & 366 & 40 & 500 & 40 & 650 & 40 & 700 & 40 \
\mathrm{r} & \mathrm{MHZ} & & \mathrm{MHZ} & & \$ \mathrm{MHZ} & & \$ 7 \% & \
& \$ 175 & & \$ 239 & & \$ 500 & & \$ 742 & \
\hline \text { Memory } & 64 \mathrm{MB} & 40 & 96 \mathrm{MB} & 40 & 128 \mathrm{MB} & 15 & 256 \mathrm{MB} & 15 \
& \$ 95 & & \$ 189 & & \$ 250 & & \$ 496 & \
\hline \text { Hard } & 4 \mathrm{~GB} & 10 & 6 \mathrm{~GB} & 25 & 13 \mathrm{~GB} & 35 & 20 \mathrm{~GB} & 50 \
\text { Drive } & \$ 89 & & \$ 133 & & \$ 196 & & \$ 350 & \
\hline \text { Monitor } & 14 " & 3 & 15 " & 65 & 17^{\prime \prime} & 25 & 19 " 10 \
& \$ 95 & & \$ 160 & & \$ 280 & & \$ 480 & 10 \
\hline \text { Graphics } & \text { Stock } & 100 & 3-\mathrm{D} & 15 & & & & \
\text { Card } & \$ 100 & & \$ 250 & & & & & \
\hline \text { CD- } & 24 \mathrm{X} & 5 & 40 \mathrm{X} & 25 & 72 \mathrm{X} & 50 & \text { DVD } & 45 \
\text { ROM } & \$ 30 & & \$ 58 & & \$ 125 & & \$ 178\
\hline \text { Sound } & \text { Stock } & 100 & \text { Sound } & 50 & \text { Plat II } & 25 \
\text { Card } & \$ 99 & & \text { II } & \$ 150 & & \$ 195 \
\hline \text { Speakers } & \text { Stock } & 75 & 60 \mathrm{~W} & 75 & 120 \mathrm{~W} & 25 \
& \$ 29 & & \$ 69 & & \$ 119 & \
\hline \text { Modem } & \begin{array}{l}
\text { Stock } \
\$ 99
\end{array} & 125 & & \
\hline \text { Mouse } & \begin{array}{l}
\text { Stock } \
\$ 39
\end{array} & 125 & \begin{array}{l}
\text { Ergo } \
\$ 69
\end{array} & 35 \
\hline \text { Keyboar } & \text { Stock } & 100 & \text { Ergo } & 35 \
\text { d } & \$ 59 & & \$ 129 & \
\hline \text { Game } & \text { Stock } & 25 & & \
\text { Devices } & \$ 165 & & & \
\hline
\end{array}\) 
The requirements for each system are provided in the following table:
 $$\begin{array} { r r r } 
& \text { System A } & \text { System B } \
\hline \text { Proces5ar } & 366 \mathrm { MHZ } & 700 \mathrm { MHZ } \
\text { Memory } & 64 \mathrm { MB } & 96 \mathrm { MB } \
\text { Hard Drive } & 6 \mathrm {~GB} & 20 \mathrm {~GB} \
\text { Monitar } & 15 " & 15 " \
\text { Graphics Card } & \text { Stack } & \text { Stack } \
\text { CD-ROM } & 40 X & 72 X \
\text { Sound Card } & \text { Stack } & \text { Stack } \
\text { Speakers } & \text { Stack } & 60 W \
\text { Modem } & \text { Stack } & \text { Stack } \
\text { Mouse } & \text { Stack } & \text { Stack } \
\text { Keyboard } & \text { Stack } & \text { Stack }
\end{array}$$ 
Each system requires assembly,testing and packaging.The requirements per system built and resources available are summarized in the table below.
 $\begin{array}{rrrr} 
& \text { System A } & \text { System B } & \text { Total Hours Available } \
\hline \text { Assembly hours) } & 2.25 & 2.50 & 200 \
\text { Testing hours) } & 1.25 & 2.00 & 150 \
\text { Packaging hours) } & 050 & 0.50 & 75
\end{array}$ 
Joey is uncertain about product demand.In the past he has put together similar types of computer packages but his sales results vary.As a result is unwilling to commit all his in-house labor force to building the computer packages.He is confident he can sell all he can build and is not overly concerned with lost sales due to stock-outs.Based on his market survey,he has completed his advertising flyer and will offer System A for $ 1250 and will offer system B for
$ 2325.Joey now needs to let his workers know how many of each system to build and he wants that mix to maximize his profits.
Formulate an LP for Dave's problem.Solve the model using the graphical method.What is Dave's preferred product mix? What profit does Dave expect to make from this product mix?

Accepted Answer

The cost to make System A is $1007 while

Question 20

The symbols X1,Z1,Dog are all examples of

Accepted Answer

A) decision variables. 
B) constraints. 
C) objectives. 
D) parameters. 
A) decision variables. 
B) constraints. 
C) objectives. 
D) parameters.

If a problem has infinite number solutions,the objective function

The second step in formulating a linear programming problem is

This graph shows the feasible region defined by points ACDEF)and objective function level curve BG)for a maximization problem.Which point corresponds to the optimal solution to the problem?

The following diagram shows the constraints for a LP model.Assume the point 0,0)satisfies constraint B,J)but does not satisfy constraints D,H)or C,I).Which set of points on this diagram defines the feasible solution space?

A facility produces two products.The labor constraint in hours)is formulated as: 350x₁+300x₂≤ 10,000.The Number 10,000 represents

When do alternate optimal solutions occur in LP models?

A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced.Which of the following constraints reflects this fact?

Level curves are used when solving LP models using the graphical method.To what part of the model do level curves relate?

Which of the following actions would expand the feasible region of an LP model?

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

The objective function for a LP model is 3 X₁+ 2 X₂.If X₁= 20 and X₂= 30,what is the value of the objective function?

A company uses 4 pounds of resource 1 to make each unit of X₁and 3 pounds of resource 1 to make each unit of X₂.There are only 150 pounds of resource 1 available.Which of the following constraints reflects the relationship between X₁,X₂and resource 1?

The first step in formulating a linear programming problem is

The constraint for resource 1 is 5 X₁+ 4 X₂≤ 200.If X₁= 20 and X₂= 5,how much of resource 1 is unused?

The symbols X₁,Z₁,Dog are all examples of

Introduction to Modeling and Decision Analysis

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

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 2: Introduction to Optimization and Linear Programming

If a problem has infinite number solutions,the objective function

The second step in formulating a linear programming problem is

This graph shows the feasible region defined by points ACDEF)and objective function level curve BG)for a maximization problem.Which point corresponds to the optimal solution to the problem?

The following diagram shows the constraints for a LP model.Assume the point 0,0)satisfies constraint B,J)but does not satisfy constraints D,H)or C,I).Which set of points on this diagram defines the feasible solution space?

A facility produces two products.The labor constraint in hours)is formulated as: 350x1+300x2 ≤ 10,000.The Number 10,000 represents

When do alternate optimal solutions occur in LP models?

A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced.Which of the following constraints reflects this fact?

Level curves are used when solving LP models using the graphical method.To what part of the model do level curves relate?

Which of the following actions would expand the feasible region of an LP model?

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

The objective function for a LP model is 3 X1 + 2 X2.If X1 = 20 and X2 = 30,what is the value of the objective function?

A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2.There are only 150 pounds of resource 1 available.Which of the following constraints reflects the relationship between X1,X2 and resource 1?

The first step in formulating a linear programming problem is

The constraint for resource 1 is 5 X1 + 4 X2 ≤ 200.If X1 = 20 and X2 = 5,how much of resource 1 is unused?

The symbols X1,Z1,Dog are all examples of

Introduction to Modeling and Decision Analysis

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

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

A facility produces two products.The labor constraint in hours)is formulated as: 350x₁+300x₂≤ 10,000.The Number 10,000 represents

The objective function for a LP model is 3 X₁+ 2 X₂.If X₁= 20 and X₂= 30,what is the value of the objective function?

A company uses 4 pounds of resource 1 to make each unit of X₁and 3 pounds of resource 1 to make each unit of X₂.There are only 150 pounds of resource 1 available.Which of the following constraints reflects the relationship between X₁,X₂and resource 1?

The constraint for resource 1 is 5 X₁+ 4 X₂≤ 200.If X₁= 20 and X₂= 5,how much of resource 1 is unused?

The symbols X₁,Z₁,Dog are all examples of