1. A computer implemented method of determining an optimized rate value of a target product in a financial system, comprising: providing a plurality of products in the financial system, each of the plurality of products defined by a set of attributes and associated values; defining, by a processor, for each of the plurality of products, associated product rules for the plurality of products that impact a rate value of the plurality of products, each of the associated product rules being one of linear rules or rules reducible to a linear form and relating to two of the plurality of products, the defining of the associated product rules comprising: specifying the attributes and an attribute hierarchy for each of the associated product rules; specifying a rule type for each of the specified attributes; specifying a direction of a rate movement direction for the specified attributes; and specifying a gap value for each of the specified attributes; defining a set of rules that preserves the relationships between the associated products specified by the associated product rules, at least some of the set of rules being mathematically induced from the associated product rules; and optimizing, by the processor, the set of rules to produce an optimized scenario, wherein the optimizing comprises: applying the set of rules to the plurality of products that actively contribute to a key product indicator; performing densification to infer the optimized rate value for each of the plurality of products which do not actively contribute to the key product indicator; determining that a starting rate of one of the plurality of products violates the first associated product rule; relaxing the starting rate of one of the plurality of products in response to the determining; and providing an output including a recommendation of the optimized rate value for the target product to achieve a target in the optimized scenario, wherein the target includes a profit value and a sales volume value.