Sensitivity analysis is like checking how much a small change in a rule affects the best answer, which helps us make smart choices when things are uncertain or resources are limited. While, the shadow prices are like telling us the exact value we would get if we had a little more of something, showing us where it's most important to use resources wisely for the best result.

Sensitivity analysis involves calculating the range of allowable parameter values for which the optimal solution remains unchanged, either by changing one parameter at a time or using more advanced techniques like the simplex method. Shadow prices are calculated through the dual formulation of the linear programming problem. The optimal dual solution provides the shadow prices for the constraints.

Sensitivity analysis is applicable to a wide range of optimization problems and is particularly useful when there's uncertainty or variability in the input parameters, allowing decision-makers to make informed decisions under various scenarios. Shadow prices are primarily relevant in problems where resources are constrained and decisions involve trade-offs between different constraints. They assist in determining the optimal allocation of limited resources to achieve the best possible outcomes.

Sensitivity analysis helps us make wise decisions when circumstances are unknown or resources are scarce by measuring the impact of a modest modification in a rule on the optimal solution. While the shadow prices show us where it's most crucial to spend resources effectively for the best outcome, they are similar to informing us the exact value we would obtain if we had a little bit more of anything.

Sensitivity analysis focuses on understanding the impact of changes in model parameters, while shadow price measures the rate of improvement in the objective function value per unit increase in a constraint's bound. Sensitivity analysis provides a broader understanding of the model, while shadow price provides specific information about the impact of constraints on the objective function.