A fundamental basis change happens when a resource change causes a basic variable to hit zero and try to go negative, requiring a dual simplex pivot rather than a simple value update.

A fundamental basis change occurs when the RHS change goes beyond its allowable range, causing the current basic solution to become infeasible or changing the optimal basis.

If the new RHS goes outside its allowable range, the current basis may change; if it stays within the allowable range, the basis remains the same and only the objective value changes based on the shadow price.

The key is the allowable RHS range from the final simplex tableau.

A change in a right-hand-side value causes a fundamental basis change whenever the updated value causes any basic variable to become negative in the current optimal solution.

You know an RHS change causes a basis change when it pushes any basic variable's value below zero, violating primal feasibility and forcing a transition to a new corner point.

A basis change occurs when altering an RHS value causes a basic variable's optimal value to cross zero and become negative, violating primal feasibility.

You can check the allowable increase and allowable decrease of the RHS value in the sensitivity analysis. If the RHS change stays within this range, the current basis remains the same and only the objective value changes. If the change goes beyond the allowable range, the basis may change and the problem should be solved again.

A fundamental basis change occurs when the new right-hand-side value falls outside its calculated allowable increase or allowable decrease range. As long as the change remains inside this range, the set of basic variables stays identical and only the objective value shifts proportionally by the shadow price. The moment the change exceeds the allowable limits, a current basic variable drops to zero and becomes non-basic, forcing a new variable into the basis and rendering the old shadow price invalid.

A change within the allowable range keeps the current optimal basis intact, causing the values of the basic variables and the objective function to adjust predictably via the shadow price. A change outside the allowable range causes a basic variable to violate feasibility, forcing a fundamental basis change via a dual simplex pivot to restore feasibility.

A change in the RHS causes a fundamental basis change when it moves outside the allowable RHS range, causing a basic variable to reach zero or violate feasibility; within the allowable range, the basis remains unchanged.

You can tell by checking the allowable increase and decrease of the RHS in the sensitivity analysis. If the new RHS stays within this range, the current basis remains valid and only the objective value changes; if it goes outside the range, the basis may change and the shadow price may no longer apply.

A change in an RHS value causes only a shift in the objective value if it stays within its allowable range; if it goes outside the allowable range, the current basis may change and the optimal solution must be re-evaluated.

Check the sensitivity analysis report for the allowable increase and decrease of the RHS value. If the change stays within this range, the current basis remains valid and only the objective value changes. If it goes beyond the range, the basis may change and the problem needs to be re-evaluated.