Question 1

According to studies mentioned in Chapter 3, linear programming algorithms are considered to be one of the top 10 most important tools of the last century.

Accepted Answer

Linear programming algorithms have indeed been recognized as one of the top 10 most important tools of the last century due to their wide applicability in various fields such as economics, military, and transportation for optimizing resource allocation.

Question 2

In a linear programming model, the decision maker always seeks to maximize the objective function.

Accepted Answer

In a linear programming model, the decision maker may seek to either maximize or minimize the objective function, depending on the problem's goal (e.g., maximizing profit or minimizing cost).

Question 3

Technological coefficients represent the usage of a given resource per each unit of the decision variable.

Accepted Answer

Technological coefficients in linear programming models indicate the amount of a resource consumed or used by each unit of a decision variable.

Question 4

A pivot table is a data summarization tool in Microsoft Excel and other business intelligence software.

Accepted Answer

A pivot table allows users to automatically sort, count, and total the data stored in one table or spreadsheet and create a second table displaying the summarized data.

Question 5

Suppose that the right-hand-side value of a given binding constraint is increased by one unit and within the lower and upper limit. Instead of rerunning the solution, the decision maker can simply check the shadow price to know the exact change of the objective function.

Accepted Answer

The shadow price reflects the rate of improvement in the objective function value for a one-unit increase in the right-hand-side value of a binding constraint, assuming other conditions remain constant.

Question 6

Suppose that the right-hand-side value of a given binding constraint is increased by one unit and within the lower and upper limit. Instead of rerunning the solution, the decision maker can simply check the shadow price and know the exact change of the objective function.

Accepted Answer

The shadow price reflects the change in the objective function value per unit increase in the right-hand side of a binding constraint, assuming other conditions remain constant and the change is within the limits of the current basis.

Question 7

The reduced cost for a decision variable is the shadow price of the constraint for that variable.

Accepted Answer

The reduced cost of a decision variable is the amount by which the objective function would improve if the variable were increased by one unit, holding all other variables constant. The shadow price of a constraint is the amount by which the objective function would improve if the constraint were relaxed by one unit. Therefore, the reduced cost of a decision variable is the shadow price of the constraint for that variable.

Question 8

Linear programming model constraints are mostly less than or equal to constraints.

Accepted Answer

The answer of Linear programming model constraints are mostly less...

Question 9

Linear programming model constraints are mostly greater than or equal to constraints.

Accepted Answer

Linear programming model constraints can be of three types: less than or equal to, greater than or equal to, or equal to, depending on the specific requirements of the problem being modeled.

Question 10

When incorporating a large amount of input data, the decision maker must calculate model parameters as an additional step in the process of formulating a linear programming model.

Accepted Answer

When incorporating a large amount of input data, the decision maker must calculate model parameters as an additional step in the process of formulating a linear programming model. This is because the model parameters are used to represent the relationships between the decision variables and the objective function, and they must be calculated in order to ensure that the model is accurate and can be used to make effective decisions.

Question 11

When incorporating a large amount of input data, formulating the objective function is an additional step in the process of formulating a linear programming model.

Accepted Answer

The formulation of the objective function is a fundamental step in the process of formulating a linear programming model, regardless of the amount of input data. The objective function defines the goal of the optimization, such as maximizing profit or minimizing cost, and is essential for solving the problem.

Question 12

During sensitivity analysis, the shadow price indicates the maximum value of contribution coefficients that will not alter the value of the objective function.

Accepted Answer

The shadow price in sensitivity analysis represents the amount by which the value of the objective function would change with a one-unit increase in the right-hand side value of a constraint, not the contribution coefficients.

Question 13

During sensitivity analysis, the shadow price indicates the minimum value of contribution coefficients that will not alter the value of the objective function.

Accepted Answer

The shadow price in sensitivity analysis actually represents the rate of improvement in the objective function value for a one-unit increase in the right-hand side value of a constraint, not the minimum value of contribution coefficients.

Question 14

During sensitivity analysis, the shadow price indicates the value of the objective function changes when one additional unit of the respective constraint is acquired.

Accepted Answer

The shadow price in sensitivity analysis represents the rate at which the objective function's value changes as a result of a one-unit increase in the right-hand side of a constraint, assuming all else remains constant.

Question 15

If the right-hand-side value of a binding constraint is increased by one unit, then the objective function will change in an amount equal to the value of the reduced cost.

Accepted Answer

The change in the objective function value due to a one-unit increase in the right-hand-side value of a binding constraint is equal to the shadow price or dual value of that constraint, not the reduced cost, which is associated with the objective function coefficients of decision variables.

Question 16

If the right-hand-side value of a binding constraint is increased by one unit, then the objective function will change in an amount equal to the shadow price.

Accepted Answer

The shadow price represents the rate of improvement in the objective function value for a one-unit increase in the right-hand-side value of a binding constraint, assuming all else remains constant.

Question 17

A magnetic system approach allows data scientists to incorporate only selected sources of data as input values in a linear programming model.

Accepted Answer

A magnetic system approach is not a recognized method for selecting data sources in linear programming models. Linear programming involves mathematical techniques for optimizing a particular outcome based on given constraints, and data selection is based on relevance and accuracy, not a "magnetic system."

Question 18

An agile system has the ability to produce and adapt data from heterogeneous sources.

Accepted Answer

Agile systems are designed to be flexible and adaptable, allowing them to efficiently handle and integrate data from various sources, regardless of the differences in data format or structure.

Question 19

The implementation of LP models in the era of Big Data requires that data scientists consider a trade-off between less-than-optimal but practical solutions and optimal-but-complex and often delayed solutions.

Accepted Answer

In the era of Big Data, the sheer volume and complexity of data can make finding the optimal solution for Linear Programming (LP) models computationally intensive and time-consuming. Therefore, data scientists often have to balance between achieving a less-than-optimal solution that is practical and can be implemented quickly, and striving for the optimal solution which may be more complex and take longer to find. This trade-off is crucial for timely decision-making and resource allocation in many real-world applications.

Question 20

Which of the following is a business situation in which linear programming models can be used?
A) Determining a crop rotation policy in agriculture
B) Determining an optimal subsidy management for farmers
C) Optimizing water networks
D) All of the above

Accepted Answer

Linear programming can be applied to various optimization problems, including crop rotation policies, subsidy management, and water network optimization.

Quiz 3: Business Analytics With Linear Programming