Question 1

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 2

The constraint for resource 1 is 5 X1 + 4 X2 $\ge$ 200. If X2 = 20, what it the minimum value for X1?

Accepted Answer

A) 20 
B) 24 
C) 40 
D) 50 
A) 20 
B) 24 
C) 40 
D) 50

Question 3

Limited resources are modeled in optimization problems as

Accepted Answer

A) an objective function. 
B) constraints. 
C) decision variables. 
D) alternatives. 
A) an objective function. 
B) constraints. 
C) decision variables. 
D) alternatives.

Question 4

The constraint for resource 1 is 5 X1 + 4 X2 $\le$ 200. If X1 = 20, what it the maximum value for X2?

Accepted Answer

A) 20 
B) 25 
C) 40 
D) 50 
A) 20 
B) 25 
C) 40 
D) 50

Question 5

A common objective when manufacturing printed circuit boards is

Accepted Answer

A) maximizing the number of holes drilled. 
B) maximizing the number of drill bit changes. 
C) minimizing the number of holes drilled. 
D) minimizing the total distance the drill bit must be moved. 
A) maximizing the number of holes drilled. 
B) maximizing the number of drill bit changes. 
C) minimizing the number of holes drilled. 
D) minimizing the total distance the drill bit must be moved.

Question 6

What most motivates a business to be concerned with efficient use of their resources?

Accepted Answer

A) Resources are limited and valuable. 
B) Efficient resource use increases business costs. 
C) Efficient resources use means more free time. 
D) Inefficient resource use means hiring more workers. 
A) Resources are limited and valuable. 
B) Efficient resource use increases business costs. 
C) Efficient resources use means more free time. 
D) Inefficient resource use means hiring more workers.

Question 7

A redundant constraint is one which

Accepted Answer

A) plays no role in determining the feasible region of the problem. 
B) is parallel to the level curve. 
C) is added after the problem is already formulated. 
D) can only increase the objective function value. 
A) plays no role in determining the feasible region of the problem. 
B) is parallel to the level curve. 
C) is added after the problem is already formulated. 
D) can only increase the objective function value.

Question 8

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is

Accepted Answer

A) a feasible solution. 
B) an optimal solution. 
C) a corner point solution. 
D) both (a) and (c). 
A) a feasible solution. 
B) an optimal solution. 
C) a corner point solution. 
D) both (a) and (c).

Question 9

The constraint for resource 1 is 5 X1 + 4 X2 $\le$ 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 10

Which of the following fields of management science finds the optimal method of using resources to achieve the objectives of a business?

Accepted Answer

A) Simulation 
B) Regression 
C) Mathematical programming 
D) Discriminant analysis 
A) Simulation 
B) Regression 
C) Mathematical programming 
D) Discriminant analysis

Question 11

What are the three common elements of an optimization problem?

Accepted Answer

A) objectives, resources, goals. 
B) decisions, constraints, an objective. 
C) decision variables, profit levels, costs. 
D) decisions, resource requirements, a profit function. 
A) objectives, resources, goals. 
B) decisions, constraints, an objective. 
C) decision variables, profit levels, costs. 
D) decisions, resource requirements, a profit function.

Question 12

A common objective in the product mix problem is

Accepted Answer

A) maximizing cost. 
B) maximizing profit. 
C) minimizing production time. 
D) maximizing production volume. 
A) maximizing cost. 
B) maximizing profit. 
C) minimizing production time. 
D) maximizing production volume.

Question 13

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

Obj = 50.2

Question 14

When the objective function can increase without ever contacting a constraint the LP model 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 15

A mathematical programming application employed by a shipping company is most likely

Accepted Answer

A) a product mix problem. 
B) a manufacturing problem. 
C) a routing and logistics problem. 
D) a financial planning problem. 
A) a product mix problem. 
B) a manufacturing problem. 
C) a routing and logistics problem. 
D) a financial planning problem.

Question 16

What is the goal in optimization?

Accepted Answer

A) Find the decision variable values that result in the best objective function and satisfy all constraints. 
B) Find the values of the decision variables that use all available resources. 
C) Find the values of the decision variables that satisfy all constraints. 
D) None of these. 
A) Find the decision variable values that result in the best objective function and satisfy all constraints. 
B) Find the values of the decision variables that use all available resources. 
C) Find the values of the decision variables that satisfy all constraints. 
D) None of these.

Question 17

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 $\ge$ 100 
B) 20 A + 30 B $\le$  100 
C) 20 A + 30 B = 100 
D) 20 A = 100 
A) 20 A + 30 B $\ge$ 100 
B) 20 A + 30 B $\le$  100 
C) 20 A + 30 B = 100 
D) 20 A = 100

Question 18

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation?

Accepted Answer

A) Alternate optimum solutions and infeasibility. 
B) Redundant constraints and unbounded solutions. 
C) Infeasibility and unbounded solutions. 
D) Alternate optimum solutions and redundant constraints. 
A) Alternate optimum solutions and infeasibility. 
B) Redundant constraints and unbounded solutions. 
C) Infeasibility and unbounded solutions. 
D) Alternate optimum solutions and redundant constraints.

Question 19

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

Obj = 74.8

Question 20

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

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

The constraint for resource 1 is 5 X₁ + 4 X₂ $\ge$ 200. If X₂ = 20, what it the minimum value for X₁?

Limited resources are modeled in optimization problems as

The constraint for resource 1 is 5 X₁ + 4 X₂ $\le$ 200. If X₁ = 20, what it the maximum value for X₂?

A common objective when manufacturing printed circuit boards is

What most motivates a business to be concerned with efficient use of their resources?

A redundant constraint is one which

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is

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

Which of the following fields of management science finds the optimal method of using resources to achieve the objectives of a business?

What are the three common elements of an optimization problem?

A common objective in the product mix problem is

Solve the following LP problem graphically by enumerating the corner points.

When the objective function can increase without ever contacting a constraint the LP model is said to be

A mathematical programming application employed by a shipping company is most likely

What is the goal in optimization?

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation?

Solve the following LP problem graphically by enumerating the corner points.

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?

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

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 2: Introduction to Optimization and Linear Programming

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

The constraint for resource 1 is 5 X1 + 4 X2 ≥\ge≥ 200. If X2 = 20, what it the minimum value for X1?

Limited resources are modeled in optimization problems as

The constraint for resource 1 is 5 X1 + 4 X2 ≤\le≤ 200. If X1 = 20, what it the maximum value for X2?

A common objective when manufacturing printed circuit boards is

What most motivates a business to be concerned with efficient use of their resources?

A redundant constraint is one which

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is

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

Which of the following fields of management science finds the optimal method of using resources to achieve the objectives of a business?

What are the three common elements of an optimization problem?

A common objective in the product mix problem is

Solve the following LP problem graphically by enumerating the corner points.

When the objective function can increase without ever contacting a constraint the LP model is said to be

A mathematical programming application employed by a shipping company is most likely

What is the goal in optimization?

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation?

Solve the following LP problem graphically by enumerating the corner points.

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?

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

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

The constraint for resource 1 is 5 X₁ + 4 X₂ $\ge$ 200. If X₂ = 20, what it the minimum value for X₁?

The constraint for resource 1 is 5 X₁ + 4 X₂ $\le$ 200. If X₁ = 20, what it the maximum value for X₂?

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