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# Solve The Linear Programming Problem Multi-objective optimization is an alternative to a cost-benefit analysis that allows us to analyze decisions that have multiple, conflicting objectives without conversion to a common currency.

Linear programming (LP) is a special form of multi-objective optimization, where the objectives and constraints that describe a decision are represented by linear equations, which are then used to find the best (optimal) solutions.

The following statements use syntax that is remarkably similar to the mathematical formulation of the problem: The OPTMODEL procedure prints two tables.

The first (not shown) is a table that describes the algorithm that was used to solve the problem.

The second table is the solution vector, which is x = .  The theory of linear programming says that an optimal solution will always be found at a vertex of the feasible region, which in 2-D is a polygon.

Linear programming can be divided into seven steps. Maybe your mother wants to be a named stakeholder in this decision because she likes to see you be productive.

The first five are about defining the problem to be solved, which may be more important than the mathematics. The simple example here will be that we want a time budget for our daily activities. But, let's just focus on you as the single stakeholder. Some common objectives are to minimize costs or maximize productivity.

The LPSOLVE subroutine supports many features that are not mentioned here. The LPSOLVE subroutine was introduced in SAS/IML 13.1, which was shipped with SAS 9.4m1.

The LPSOLVE function replaces the older LP subroutine, which is deprecated.

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