A) tell how much or how many of something to produce, invest, purchase, hire, etc. B) represent the values of the constraints. C) measure the objective function. D) must exist for each constraint. A) tell how much or how many of something to produce, invest, purchase, hire, etc. B) represent the values of the constraints. C) measure the objective function. D) must exist for each constraint.

Exam 7: Introduction to Linear Programming

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain. Min 1x+1y s.t. 5x+3y\leq30 3x+4y\geq36 y\leq7 x,y\geq0

(Essay)

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Question 21

Solve the following linear program by the graphical method. Max 4x+5y s.t. x+3y\leq22 -x+y\leq4 y\leq6 2x-5y\leq0 x,y\geq0

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Question 22

The standard form of a linear programming problem will have the same solution as the original problem.

(True/False)

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Question 23

Only binding constraints form the shape (boundaries)of the feasible region.

(True/False)

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Question 24

Muir Manufacturing produces two popular grades of commercial carpeting among its many other products.In the coming production period,Muir needs to decide how many rolls of each grade should be produced in order to maximize profit.Each roll of Grade X carpet uses 50 units of synthetic fiber,requires 25 hours of production time,and needs 20 units of foam backing.Each roll of Grade Y carpet uses 40 units of synthetic fiber,requires 28 hours of production time,and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160.In the coming production period,Muir has 3000 units of synthetic fiber available for use.Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility).The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem.

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Question 25

Explain the concepts of proportionality,additivity,and divisibility.

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Question 26

An infeasible problem is one in which the objective function can be increased to infinity.

(True/False)

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Question 27

The point (3,2)is feasible for the constraint 2x₁ + 6x₂  30.

(True/False)

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Question 28

Explain what to look for in problems that are infeasible or unbounded.

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Question 29

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.

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Question 30

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

(True/False)

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Question 31

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

(True/False)

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Question 32

Decision variables

(Multiple Choice)

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Question 33

Find the complete optimal solution to this linear programming problem. Min 3x+3y s.t. 12x+4y\geq48 10x+5y\geq50 4x+8y\geq32 x,y\geq0

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Question 34

Explain the difference between profit and contribution in an objective function.Why is it important for the decision maker to know which of these the objective function coefficients represent?

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Question 35

The Sanders Garden Shop mixes two types of grass seed into a blend.Each type of grass has been rated (per pound)according to its shade tolerance,ability to stand up to traffic,and drought resistance,as shown in the table.Type A seed costs $1 and Type B seed costs $2.If the blend needs to score at least 300 points for shade tolerance,400 points for traffic resistance,and 750 points for drought resistance,how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost? Type A Type B Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5

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Question 36

It is possible to have exactly two optimal solutions to a linear programming problem.

(True/False)

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Question 37

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

(True/False)

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Question 38

All linear programming problems have all of the following properties except

(Multiple Choice)

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Question 39

The constraint 2x₁  x₂ = 0 passes through the point (200,100).

(True/False)

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Question 40

Showing 21 - 40 of 60

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain. Min 1x+1y s.t. 5x+3y\leq30 3x+4y\geq36 y\leq7 x,y\geq0

Solve the following linear program by the graphical method. Max 4x+5y s.t. x+3y\leq22 -x+y\leq4 y\leq6 2x-5y\leq0 x,y\geq0

The standard form of a linear programming problem will have the same solution as the original problem.

Only binding constraints form the shape (boundaries)of the feasible region.

Explain the concepts of proportionality,additivity,and divisibility.

An infeasible problem is one in which the objective function can be increased to infinity.

The point (3,2)is feasible for the constraint 2x₁ + 6x₂  30.

Explain what to look for in problems that are infeasible or unbounded.

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.

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

Decision variables

Find the complete optimal solution to this linear programming problem. Min 3x+3y s.t. 12x+4y\geq48 10x+5y\geq50 4x+8y\geq32 x,y\geq0

Explain the difference between profit and contribution in an objective function.Why is it important for the decision maker to know which of these the objective function coefficients represent?

It is possible to have exactly two optimal solutions to a linear programming problem.

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

All linear programming problems have all of the following properties except

The constraint 2x₁  x₂ = 0 passes through the point (200,100).

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 7: Introduction to Linear Programming

Does the following linear programming problem exhibit infeasibility,unboundedness,or alternate optimal solutions? Explain. Min 1x+1y s.t. 5x+3y\leq30 3x+4y\geq36 y\leq7 x,y\geq0

Solve the following linear program by the graphical method. Max 4x+5y s.t. x+3y\leq22 -x+y\leq4 y\leq6 2x-5y\leq0 x,y\geq0

The standard form of a linear programming problem will have the same solution as the original problem.

Only binding constraints form the shape (boundaries)of the feasible region.

Explain the concepts of proportionality,additivity,and divisibility.

An infeasible problem is one in which the objective function can be increased to infinity.

The point (3,2)is feasible for the constraint 2x1 + 6x2  30.

Explain what to look for in problems that are infeasible or unbounded.

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.

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

Decision variables

Find the complete optimal solution to this linear programming problem. Min 3x+3y s.t. 12x+4y\geq48 10x+5y\geq50 4x+8y\geq32 x,y\geq0

Explain the difference between profit and contribution in an objective function.Why is it important for the decision maker to know which of these the objective function coefficients represent?

It is possible to have exactly two optimal solutions to a linear programming problem.

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

All linear programming problems have all of the following properties except

The constraint 2x1  x2 = 0 passes through the point (200,100).

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility and Game Theory

Times Series Analysis and Forecasting

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

The point (3,2)is feasible for the constraint 2x₁ + 6x₂  30.

The constraint 2x₁  x₂ = 0 passes through the point (200,100).