The Budget Split That Explains Itself

Budget allocation is a constrained optimization problem where simple linear programming often defaults to funding a single best channel. A common fix using binary on/off variables forces diversification but converts the model to a mixed-integer program, losing the explanatory power of 'shadow prices.' A better approach models diminishing returns by slicing budgets into bands with decreasing yields, which keeps the problem as a continuous LP. This method preserves the ability to interpret the shadow prices of constraints, revealing the cost or benefit of rules like minimum spend floors.