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lowest-cost feasible supplier mix that covers all my SKU requirements."},{"title":"Ad budget allocation across channels","prompt":"I have a $50,000 monthly ad budget, six marketing channels with estimated CPAs and reach caps, and a rule that at least 30% must go to brand-safe channels — what's the highest-value allocation and how optimal is the solution?"}],"resultDescription":"Returns the optimal or best-feasible allocation/assignment decision, the objective value achieved (cost or value), independently verified feasibility evidence for the solution, and solver metadata including optimality status and gap from the theoretical optimum.","failureModes":["Infeasible problem — no combination satisfies all constraints simultaneously, solver returns infeasibility certificate","Timeout/gap too large — problem is too large to solve to optimality within limits, returns best incumbent with gap","Malformed input — missing required fields like options or constraints causes a 400-level 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