Question 1

The term "allowable range for the right-hand-side" refers to coefficients of the objective function.

Accepted Answer

The term "allowable range for the right-hand-side" refers to the range of values that the coefficients in the constraints can take without changing the optimal solution.

Question 2

The purpose of a linear programming study is to help guide management's final decision by providing insights.

Accepted Answer

Linear programming provides quantitative analysis and optimization to help management make informed decisions. It helps identify the best possible solutions out of the available options based on the constraints and objectives specified by the decision-makers. Therefore, the purpose of a linear programming study is to provide insights and facilitate decision-making.

Question 3

It is usually quite easy to find the needed data for a linear programming study.

Accepted Answer

Sometimes the data needed for a linear programming study can be difficult or time-consuming to obtain. It may require conducting surveys, collecting data from multiple sources, or making assumptions and estimates.

Question 4

Changing the objective function coefficients may or may not change the optimal solution,but it will always change the value of the objective function.

Accepted Answer

Changing the objective function coefficients can indeed change the optimal solution, but it does not always change the value of the objective function. If the change does not affect the constraints' binding status or the feasible region's shape in a way that influences the optimal solution, the value of the objective function might remain unchanged.

Question 5

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

Accepted Answer

The allowable range for an objective function coefficient refers to the range or values that a coefficient of a decision variable in the objective function can take without affecting the optimal solution. It is not related to the right-hand side quantity of a constraint.

Question 6

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

Accepted Answer

Not every change in the value of an objective function coefficient will lead to a changed optimal solution because the solution space and optimal vertex can remain unchanged for certain ranges of coefficient values, a concept known as the range of optimality in linear programming.

Question 7

If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function,then management will want to take special care to narrow this estimate down.

Accepted Answer

If the optimal solution remains the same over a wide range of values for a particular coefficient in the objective function, management may not need to narrow down the estimate for that coefficient as it may not have a significant impact on the optimal solution.

Question 8

When maximizing profit in a linear programming problem,the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change.

Accepted Answer

The answer of When maximizing profit in a linear programming...

Question 9

A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution.

Accepted Answer

A shadow price actually tells us how much the objective function's value will change if the right-hand side of a constraint is increased by one unit, assuming all else remains constant. It does not directly indicate how much a decision variable can be increased or decreased without changing the solution's value.

Question 10

If the change to a right-hand side is within the allowable range,the solution will remain the same.

Accepted Answer

The basic solution may remain feasible, but the optimal solution could change because the allowable range only guarantees that the current basis remains optimal, not that the solution values stay the same.

Question 11

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

Accepted Answer

Shadow price analysis is a tool used to determine the impact of changing certain factors, such as resources or constraints, on the optimal solution of a problem. It helps management find the best trade-off between costs and benefits by computing the shadow prices, which indicate the value of additional resources or the cost of reducing constraints. Therefore, the statement is true.

Question 12

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

Accepted Answer

This is a correct definition of shadow price.

Question 13

According to the 100% rule for simultaneous changes in objective function coefficients,if the sum of the percentage changes exceeds 100%,the optimal solution definitely will change.

Accepted Answer

The 100% rule for simultaneous changes in objective function coefficients states that if the sum of the absolute values of the percentage changes in the coefficients (weighted by their respective allowable increases and decreases) does not exceed 100%, the current optimal solution remains optimal. Exceeding 100% does not guarantee a change; it only indicates the potential for change, requiring further analysis.

Question 14

If the change to a right-hand side is within the allowable range,the value of the shadow price remains valid.

Accepted Answer

When the change to a right-hand side is within the allowable range, the shadow price remains valid as it represents the change in the objective function value per unit increase in the right-hand side of the constraint.

Question 15

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

Accepted Answer

The allowable range for an objective function coefficient in linear programming is calculated under the assumption that the estimates for all other coefficients in the model are accurate and fixed. This range indicates how much the coefficient can vary without changing the optimal solution, assuming all other coefficients remain unchanged.

Question 16

The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal.

Accepted Answer

The allowable range or sensitivity range in linear programming refers to the range of values that the coefficients of the objective function can take without changing the optimal solution's decision variables.

Question 17

Whenever proportional changes are made to all the unit profits in a problem,the optimal solution will remain the same.

Accepted Answer

This is because the relative differences between the unit profits remain the same, and thus the rankings of the units in terms of profitability remain the same. This means that the same units will be selected for production, and the optimal solution remains unchanged.

Question 18

When certain parameters of a model represent managerial policy decisions,what-if analysis provides information about what the impact would be of altering these policy decisions.

Accepted Answer

What-if analysis is a tool that can be used to simulate the impact of changing certain variables or parameters in a model. When the parameters that are being changed represent managerial policy decisions, what-if analysis can provide valuable information about the potential impact of those decisions on the overall performance of a business or organization. This allows managers to make more informed decisions and to evaluate different scenarios before implementing any changes.

Question 19

When a change in the value of an objective function coefficient remains within the allowable range,the optimal solution will also remain the same.

Accepted Answer

This statement is true. If a change in the value of an objective function coefficient remains within the allowable range, the shadow price of the corresponding resource will change, but the optimal solution will not change. This is because the optimal solution is determined by the constraints, not just the objective function coefficients. As long as the constraints remain the same, the optimal solution will remain the same.

Question 20

An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem.

Accepted Answer

An optimal solution is obtained based on assumptions made in the mathematical model used to represent the problem, but these assumptions may not be a perfect representation of the actual problem. Therefore, the optimal solution is only optimal within the context of the model used.

Quiz 5: What-If Analysis for Linear Programming