Where does solution collide?

A value, or an assignment of values to the unknowns, that makes an equation or a system of equations true when it is substituted in. In linear algebra a solution to the system Ax = b is any vector x that satisfies every equation at once, and the collection of all such vectors is the solution set, which may be empty, a single point, or infinite. Strang's Introduction to Linear Algebra develops when such solutions exist and how they are found by elimination. The referent is an abstract object that satisfies a stated relation, with no sense in which one solution is better than another, unlike a chosen answer to an optimisation problem, a dissolved mixture, or a commercial offering.[1]

Unit

A value or vector that satisfies an equation or system

Recovery means

Not applicable

Measured by

Verified by substituting it back into the equation, and described by the dimension of the solution set it belongs to

A candidate answer to a defined decision problem, given as an assignment of values to the decision variables. A feasible solution is one that satisfies all of the problem's constraints, and an optimal solution is a feasible one that also gives the best value of the objective, located by searching the solution space of admissible points. Dantzig's Linear Programming and Extensions set out the feasible region of a linear programme and the simplex method that moves between its vertices toward an optimum. The referent is a point selected from a space of allowed answers and ranked by an objective, not merely any value that satisfies an equation, a homogeneous mixture, or a bundle a supplier sells.[2]

Unit

A point in the feasible space, ranked by an objective function

Recovery means

Not applicable

Measured by

Judged by whether it is feasible under every constraint and by the objective value it achieves relative to the optimum

An integrated bundle of products and services assembled and sold to resolve a particular customer problem, rather than sold as separate goods from a catalogue. In solution selling a supplier diagnoses the customer's need and offers a combined, often customised, package with support, and the sale is organised around the outcome the customer is buying. Tuli, Kohli, and Bharadwaj's Rethinking Customer Solutions argued that customers experience a solution not as a bundle of goods but as a set of relational processes, and Storbacka's A Solution Business Model set out the capabilities a firm needs to deliver one. The referent is a commercial offering built around a buyer's problem, not a mixture in a flask, a value that satisfies an equation, or an optimum in a feasible region.[3][4]

Unit

A bundled product-and-service offering, priced and sold as one

Recovery means

Not applicable

Measured by

Assessed by the outcome delivered to the customer and by the revenue and margin earned on the combined offering