Question 1

Sensitivity analysis answers "what if" questions to help the decision maker.

Accepted Answer

Sensitivity analysis helps in assessing the impact of changes in input variables or assumptions on the outcome, effectively answering "what if" questions for decision-makers.

Question 2

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken one at a time, that would keep the current solution optimal.

Accepted Answer

Sensitivity analysis in linear programming allows for the assessment of how changes in the coefficients of the objective function (while changing one coefficient at a time) affect the optimality of the current solution. It helps in understanding the range within which these coefficients can vary without altering the optimal solution.

Question 3

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken two at a time, that would keep the current solution optimal.

Accepted Answer

Sensitivity analysis typically examines the effect of changes in one parameter at a time on the optimal solution, not two simultaneously.

Question 4

Sensitivity analysis could be used to estimate the range of values of the right hand side, taken one at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) - though the magnitude of the variables may change.

Accepted Answer

Sensitivity analysis in linear programming allows for the assessment of how changes in the coefficients of the constraints (right-hand side values) affect the optimal solution. It can determine the range within which these coefficients can vary without changing the basic variables in the solution, although their values might adjust.

Question 5

In a two-variable graphical linear program, if the coefficient of one of the variables in the objective function is changed (while the other remains fixed), then the slope of the objective function expression will change.

Accepted Answer

Changing the coefficient of one of the variables in the objective function will alter the ratio between the coefficients of the two variables, thereby changing the slope of the objective function line on the graph.

Question 6

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the plot of the corresponding constraint will move in parallel to its old plot.

Accepted Answer

Changing the RHS of a constraint in a linear program alters the intercept of the constraint line on the axes, causing the line to shift parallel to its original position without changing its slope.

Question 7

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the problem cannot become infeasible.

Accepted Answer

Changing the RHS of a constraint can shift its position, potentially leading to a situation where no solution satisfies all constraints simultaneously, thus making the problem infeasible.

Question 8

In a two-variable graphical linear program, if the RHS of one of the constraints is increased (keeping all other things fixed), the plot of the line will move away from the origin.

Accepted Answer

Increasing the RHS of a constraint in a linear program shifts the constraint line away from the origin, as it represents a higher value that must be satisfied by the solution.

Question 9

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken one at a time, that would keep the same variables as the current solution, in the optimal solution (same variables basic), though the magnitude of the variables may change.

Accepted Answer

Sensitivity analysis in linear programming allows for the examination of how changes in the coefficients of the constraints (while changing one coefficient at a time) affect the optimal solution. It helps in understanding the range within which these coefficients can vary without changing the set of basic variables in the solution, although the values of these variables might change.

Question 10

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken two at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) --though the magnitude of the variables may change.

Accepted Answer

The answer of Sensitivity analysis could be used to estimate...

Question 11

The value of 0 will always be included in any range produced by sensitivity analysis.

Accepted Answer

0 is always included in any range produced by sensitivity analysis because it is the lower bound of the range.

Question 12

The value of ${ }^{\infty}$ will always be included in any range produced by sensitivity analysis.

Accepted Answer

Sensitivity analysis evaluates how different values of an input variable can impact a particular output under a given set of assumptions, but it does not inherently include or result in infinite values as part of its range of outcomes.

Question 13

The value of ${ }^{\infty}$ may be included as part of the range produced by sensitivity analysis in some problems.

Accepted Answer

Sensitivity analysis can produce a range of possible outcomes, and in some cases, the value of infinity may be included as part of that range. This can occur when the model is highly sensitive to changes in input parameters, and the resulting range of outcomes is unbounded.

Question 14

If a problem has a $\leq$ constraint with a positive RHS, then increasing the RHS would leave the optimal solution's objective function value the same or improve it (i.e. increase the objective function value corresponding to the optimal solution if it is a "maximize" objective function and decrease it if it is a "minimize" objective function).

Accepted Answer

Increasing the RHS of a $\leq$ constraint generally relaxes the constraint, allowing for more feasible solutions. In a maximization problem, this can lead to a higher objective function value, as there is more "space" to find a better solution. In a minimization problem, it could potentially lead to a lower objective function value, as the solution space is expanded, possibly uncovering more efficient solutions.

Question 15

If a problem has a $\leq$ constraint with a positive RHS, then decreasing the RHS cannot improve (i.e. increase the objective function value corresponding to the optimal solution if it is a "maximize" objective function and decrease it if it is a "minimize" objective function) the objective function value.

Accepted Answer

Decreasing the RHS of a $\leq$ constraint tightens the feasible region, potentially excluding optimal solutions, which cannot improve the objective function value.

Question 16

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be ${ }^{\infty}$.

Accepted Answer

The upper limit on the range for the RHS in sensitivity analysis is not necessarily infinity, even if the resource is fully utilized in the optimal solution. The range depends on how changes in the RHS affect the feasibility and optimality of the current solution, which can be finite.

Question 17

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is not fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be $\infty$.

Accepted Answer

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is not fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be $\infty$ because the optimal solution is not sensitive to changes in the RHS.

Question 18

In a two-variable linear programming problem, if the RHS corresponding to a binding constraint were to be increased, the value of the variables corresponding to the optimal solution would also change.

Accepted Answer

In a two-variable linear programming problem, if the right-hand side (RHS) of a binding constraint is increased, the feasible region defined by the constraints is altered. Since a binding constraint directly influences the optimal solution, changing it would typically result in a shift of the optimal solution point, thereby changing the values of the variables at the optimal solution.

Question 19

In a two-variable linear programming problem, even if the RHS corresponding to a binding constraint were to be increased by a very large amount, it will always continue to be a binding constraint corresponding to the changed problem.

Accepted Answer

A binding constraint is one where the solution values exactly satisfy the constraint's equation. If the right-hand side (RHS) of a binding constraint is increased by a large amount, the constraint may no longer be binding because the solution space has expanded, potentially allowing for new optimal solutions that do not exactly satisfy the original constraint's equality.

Question 20

Shadow price of a resource corresponding to a nonbinding constraint is always 0 .

Accepted Answer

The shadow price of a resource corresponding to a nonbinding constraint is always 0 because the constraint is not limiting the solution; hence, changing the amount of this resource does not affect the objective function value.

Quiz 5: Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Sensitivity analysis answers "what if" questions to help the decision maker.

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken one at a time, that would keep the current solution optimal.

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken two at a time, that would keep the current solution optimal.

Sensitivity analysis could be used to estimate the range of values of the right hand side, taken one at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) - though the magnitude of the variables may change.

In a two-variable graphical linear program, if the coefficient of one of the variables in the objective function is changed (while the other remains fixed), then the slope of the objective function expression will change.

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the plot of the corresponding constraint will move in parallel to its old plot.

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the problem cannot become infeasible.

In a two-variable graphical linear program, if the RHS of one of the constraints is increased (keeping all other things fixed), the plot of the line will move away from the origin.

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken one at a time, that would keep the same variables as the current solution, in the optimal solution (same variables basic), though the magnitude of the variables may change.

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken two at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) --though the magnitude of the variables may change.

The value of 0 will always be included in any range produced by sensitivity analysis.

The value of ${ }^{\infty}$ will always be included in any range produced by sensitivity analysis.

The value of ${ }^{\infty}$ may be included as part of the range produced by sensitivity analysis in some problems.

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be ${ }^{\infty}$ .

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is not fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be $\infty$ .

In a two-variable linear programming problem, if the RHS corresponding to a binding constraint were to be increased, the value of the variables corresponding to the optimal solution would also change.

In a two-variable linear programming problem, even if the RHS corresponding to a binding constraint were to be increased by a very large amount, it will always continue to be a binding constraint corresponding to the changed problem.

Shadow price of a resource corresponding to a nonbinding constraint is always 0 .

Quiz 5: Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Sensitivity analysis answers "what if" questions to help the decision maker.

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken one at a time, that would keep the current solution optimal.

Sensitivity analysis could be used to estimate the range of values of the objective function coefficient, taken two at a time, that would keep the current solution optimal.

Sensitivity analysis could be used to estimate the range of values of the right hand side, taken one at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) - though the magnitude of the variables may change.

In a two-variable graphical linear program, if the coefficient of one of the variables in the objective function is changed (while the other remains fixed), then the slope of the objective function expression will change.

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the plot of the corresponding constraint will move in parallel to its old plot.

In a two-variable graphical linear program, if the RHS of one of the constraints is changed (keeping all other things fixed), then the problem cannot become infeasible.

In a two-variable graphical linear program, if the RHS of one of the constraints is increased (keeping all other things fixed), the plot of the line will move away from the origin.

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken one at a time, that would keep the same variables as the current solution, in the optimal solution (same variables basic), though the magnitude of the variables may change.

Sensitivity analysis could be used to estimate the range of values of the coefficient of the constraints, taken two at a time, that would keep the same variables as the current solution in the optimal solution (same variables basic) --though the magnitude of the variables may change.

The value of 0 will always be included in any range produced by sensitivity analysis.

The value of ∞{ }^{\infty}∞ will always be included in any range produced by sensitivity analysis.

The value of ∞{ }^{\infty}∞ may be included as part of the range produced by sensitivity analysis in some problems.

If a problem has a ≤\leq≤ constraint with a positive RHS, and if that resource is fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be ∞{ }^{\infty}∞ .

If a problem has a ≤\leq≤ constraint with a positive RHS, and if that resource is not fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be ∞\infty∞ .

In a two-variable linear programming problem, if the RHS corresponding to a binding constraint were to be increased, the value of the variables corresponding to the optimal solution would also change.

In a two-variable linear programming problem, even if the RHS corresponding to a binding constraint were to be increased by a very large amount, it will always continue to be a binding constraint corresponding to the changed problem.

Shadow price of a resource corresponding to a nonbinding constraint is always 0 .

The value of ${ }^{\infty}$ will always be included in any range produced by sensitivity analysis.

The value of ${ }^{\infty}$ may be included as part of the range produced by sensitivity analysis in some problems.

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be ${ }^{\infty}$ .

If a problem has a $\leq$ constraint with a positive RHS, and if that resource is not fully utilized in the optimal solution, then the upper limit on the range using sensitivity analysis for that RHS will be $\infty$ .