To check if the optimal solution remains unchanged under simultaneous objective coefficient updates, you divide each individual coefficient change by its corresponding allowable increase or allowable decrease depending on the direction of change. Sum these fractional changes together for all modified variables. If the total sum is less than or equal to one hundred percent, the current optimal solution is guaranteed to remain identical. If the sum exceeds one hundred percent, the current solution may no longer be optimal, requiring a re-evaluation of the tableau.

Calculate the fraction of the allowable increase or decrease used by each changed coefficient; if the sum of these ratios is less than or equal to 1.0 (100%), the current optimal solution remains valid.

The 100% rule is a sufficient test, not generally a necessary one: if the total exceeds 100%, it does not prove that the solution has become nonoptimal—it means the sensitivity report alone cannot guarantee that it remains optimal.

Calculate the ratio of each coefficient's actual change to its maximum allowable limit, sum those ratios, and verify the total does not exceed 1.

To determine if simultaneous changes to multiple objective function coefficients will preserve the current optimal solution, calculate the fractional change for each modified coefficient relative to its allowable limit. For each coefficient that increases, divide the change by its allowable increase, and for each coefficient that decreases, divide the absolute change by its allowable decrease. Add all of these individual fractional values together to get a total sum. If this sum is less than or equal to one, or one hundred percent, the current optimal corner point is guaranteed to remain optimal, though the objective function value itself will change.

Use the 100 percent rule by calculating the percentage of each coefficient change relative to its allowable increase or decrease. Add all these percentages together, and if the total is 100 percent or less, the current optimal solution is preserved.

You know the current optimal solution is preserved if the sum of the ratios of each coefficient's change to its respective allowable limit does not exceed 100%.

Calculate each coefficient's change as a percentage of its maximum allowable increase or decrease based on single-variable sensitivity analysis. If the sum of these percentage changes across all modified coefficients is less than or equal to 100% (1.0), the current optimal basic feasible solution is guaranteed to remain optimal.

Using the 100% rule, add the percentages of each coefficient change relative to its allowable change; if the total is 100% or less, the current optimal solution remains optimal.

Using the 100% rule, calculate each coefficient change as a percentage of its allowable increase or decrease and add the percentages; if the total is ≤ 100%, the current optimal solution remains optimal.

If the sum of the percentage changes in the objective coefficients is ≤ 100%, the current optimal solution is preserved; if it exceeds 100%, the current optimality is no longer guaranteed.

You can use the **100% rule** by adding the percentages of the changes in each objective function coefficient relative to its allowable increase or decrease; if the **total percentage is 100% or less**, the current optimal solution is preserved, but if it is **greater than 100%**, the current optimal solution may change.

To determine if simultaneous changes to multiple objective function coefficients preserve the current optimal solution using the 100% Rule, calculate the fractional change for each modified coefficient and sum them up.

Here is the exact step-by-step logic:

 * Find the allowable range for each changed coefficient: From your sensitivity analysis report, locate the allowable increase and allowable decrease for each objective coefficient that is being changed.

 * Calculate the fraction for each coefficient:

   * If a coefficient increases, divide the actual increase by its allowable increase.

   * If a coefficient decreases, divide the actual decrease by its allowable decrease.

 * Sum the fractions: Add all the calculated fractions together to get a total sum.

 * Apply the 100% Rule decision criteria:

   * If the total sum is less than or equal to 1 (100%): The current optimal solution is guaranteed to remain optimal.

   * If the total sum is greater than 1 (100%): The optimal solution may or may not change. The rule is inconclusive, and you must re-solve the linear program to

 be sure.

You can use the 100% Rule by calculating the percentage of each objective coefficient change relative to its allowable increase or decrease, then adding them together. If the total is ≤ 100%, the current optimal solution remains optimal; if it is > 100%, the current optimal solution may change.

Using the 100% rule, calculate the percentage change for each objective function coefficient and add them together. If the total is ≤ 100%, the current optimal solution is preserved. If it is > 100%, the optimal solution may change.