Question 1

Find the complete optimal solution to this linear programming problem.
Max
5X + 3Y
s.t.
2X + 3Y ≤ 30
2X + 5Y ≤ 40
6X − 5Y ≤ 0
X , Y ≥ 0

Accepted Answer

​ @#IMG-DLM& ​
The complete op

Question 2

Alternative optimal solutions occur when there is no feasible solution to the problem.

Accepted Answer

A) True 
 B)False

Question 3

Use this graph to answer the questions.   Max
20X + 10Y
s.t.
12X + 15Y ≤ 180
15X + 10Y ≤ 150
3X − 8Y ≤ 0
X , Y ≥ 0
​ 
a.Which area (I, II, III, IV, or V) forms the feasible region?
b.Which point (A, B, C, D, or E) is optimal?
c.Which constraints are binding?
d.Which slack variables are zero?

Accepted Answer

a.Area III is the feasible reg

Question 4

Solve the following system of simultaneous equations.
6X + 2Y = 50
2X + 4Y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.
6X...

Question 5

​Explain the steps of the graphical solution procedure for a minimization problem.

Accepted Answer

The graphical solution procedure for a m

Question 6

In a feasible problem, an equal-to constraint cannot be nonbinding.

Accepted Answer

A) True 
 B)False

Question 7

​The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Accepted Answer

A)  ​proportionality 
B)  ​additivity 
C)  ​divisibility 
D)  ​normality 
A)  ​proportionality 
B)  ​additivity 
C)  ​divisibility 
D)  ​normality

Question 8

​If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?

Accepted Answer

A)  ​300x1 + 125x2 > 4,000 
B)  ​300x1 + 125x2 1 + x2) 1 + 125x2 = 4,000 
A)  ​300x1 + 125x2 > 4,000 
B)  ​300x1 + 125x2 1 + x2) 1 + 125x2 = 4,000

Question 9

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

Accepted Answer

A) True 
 B)False

Question 10

For the following linear programming problem, determine the optimal solution by the graphical solution method. Are any of the constraints redundant? If yes, then identify the constraint that is redundant.
Max
X + 2Y
s.t.
X + Y ≤ 3
X − 2Y ≥ 0
Y ≤ 1
X, Y ≥ 0

Accepted Answer

X = 2, and Y = 1 Yes

Question 11

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

Accepted Answer

A)  at least 1. 
B)  0. 
C)  an infinite number. 
D)  at least 2. 
A)  at least 1. 
B)  0. 
C)  an infinite number. 
D)  at least 2.

Question 12

​Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in
the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to
new values.

Accepted Answer

To illustrate this concept, let's consid

Question 13

The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50).

Accepted Answer

A) True 
 B)False

Question 14

Given the following linear program:
Min
150X + 210Y
s.t.
3.8X + 1.2Y ≥ 22.8
Y ≥ 6
Y ≤ 15
45X + 30Y = 630
X, Y ≥ 0
​
Solve the problem graphically. How many extreme points exist for this problem?

Accepted Answer

Two extreme points exist (Poin

Question 15

Find the complete optimal solution to this linear programming problem.
Max
2X + 3Y
s.t.
4X + 9Y ≤ 72
10X + 11Y ≤ 110
17X + 9Y ≤ 153
X , Y ≥ 0

Accepted Answer

​ @#IMG-DLM& ​
The complete op

Question 16

A constraint that does not affect the feasible region is a

Accepted Answer

A)  non-negativity constraint. 
B)  redundant constraint. 
C)  standard constraint. 
D)  slack constraint. 
A)  non-negativity constraint. 
B)  redundant constraint. 
C)  standard constraint. 
D)  slack constraint.

Question 17

​A redundant constraint results in

Accepted Answer

A)  ​no change in the optimal solution(s) 
B)  ​an unbounded solution 
C)  ​no feasible solution 
D)  ​alternative optimal solutions 
A)  ​no change in the optimal solution(s) 
B)  ​an unbounded solution 
C)  ​no feasible solution 
D)  ​alternative optimal solutions

Question 18

Solve the following system of simultaneous equations.
6X + 4Y = 40
2X + 3Y = 20

Accepted Answer

The answer of Solve the following system of simultaneous equations.
6X...

Question 19

​Explain how to graph the line x1 − 2x2 ≥ 0.

Accepted Answer

To graph the line x - 2x ≥ 0, we first n

Question 20

Solve the following linear program graphically.
Max
5X + 7Y
s.t.
X ≤ 6
2X + 3Y ≤ 19
X + Y ≤ 8
X, Y ≥ 0

Accepted Answer

From the graph below

Exam 2: An Introduction to Linear Programming

Find the complete optimal solution to this linear programming problem. Max 5X + 3Y s.t. 2X + 3Y ≤ 30 2X + 5Y ≤ 40 6X − 5Y ≤ 0 X , Y ≥ 0

Alternative optimal solutions occur when there is no feasible solution to the problem.

Solve the following system of simultaneous equations. 6X + 2Y = 50 2X + 4Y = 20

​Explain the steps of the graphical solution procedure for a minimization problem.

In a feasible problem, an equal-to constraint cannot be nonbinding.

​The three assumptions necessary for a linear programming model to be appropriate include all of the following except

​If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?

An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.

For the following linear programming problem, determine the optimal solution by the graphical solution method. Are any of the constraints redundant? If yes, then identify the constraint that is redundant. Max X + 2Y s.t. X + Y ≤ 3 X − 2Y ≥ 0 Y ≤ 1 X, Y ≥ 0

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

​Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.

The constraint 5x1 − 2x2 ≤ 0 passes through the point (20, 50).

Given the following linear program: Min 150X + 210Y s.t. 3.8X + 1.2Y ≥ 22.8 Y ≥ 6 Y ≤ 15 45X + 30Y = 630 X, Y ≥ 0 ​ Solve the problem graphically. How many extreme points exist for this problem?

Find the complete optimal solution to this linear programming problem. Max 2X + 3Y s.t. 4X + 9Y ≤ 72 10X + 11Y ≤ 110 17X + 9Y ≤ 153 X , Y ≥ 0

A constraint that does not affect the feasible region is a

​A redundant constraint results in

Solve the following system of simultaneous equations. 6X + 4Y = 40 2X + 3Y = 20

​Explain how to graph the line x1 − 2x2 ≥ 0.

Solve the following linear program graphically. Max 5X + 7Y s.t. X ≤ 6 2X + 3Y ≤ 19 X + Y ≤ 8 X, Y ≥ 0

Introduction

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Explain the steps of the graphical solution procedure for a minimization problem.

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x₁) or 125 wiffle balls (x₂) can be produced per hour of labor, which of the following constraints reflects this situation?

Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.

The constraint 5x₁ − 2x₂ ≤ 0 passes through the point (20, 50).

Given the following linear program: Min 150X + 210Y s.t. 3.8X + 1.2Y ≥ 22.8 Y ≥ 6 Y ≤ 15 45X + 30Y = 630 X, Y ≥ 0 Solve the problem graphically. How many extreme points exist for this problem?

A redundant constraint results in

Explain how to graph the line x₁ − 2x₂ ≥ 0.