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Optimal solutions are basically used in linear programming problems. An optimal solution is always supposed to occur at a corner point on the area of feasible solution. There are chances of generation of more than one optimal solution in linear programming problems. For existence of the alternative optimal solutions, certain condition needs to be fulfilled. These conditions are- the objective function obtained should be parallel to the constraint that forms an edge or boundary on the area of the feasible solution and also the constraint should form a boundary on the area of the feasible solution which should be in the direction of the optimal movement of the objective function. This implies that the constraint must be a binding constraint which restricts the further improvement in the value of the objective function. The detail description and analysis of Alternative optimal solutions is given by Alternative optimal solutions Assignment Help Online.
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• Non-existing feasible solution: – We face such a situation when there is no point in the solution space satisfying all the constraints and their values. Here there are chances of the constraints being contradictory or the possibilities of inconsistencies within the constraints. Therefore the feasible solution space is found to be empty and the problem has no feasible graphical approach.
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• Unrestricted variables: – We know that till now we have made the restrictions for the decision variables to be non-negative in maximum number of practical or real life problems. But situations may arise in which the context will change and this may not always be the case. Most of the times the Simplex method assumes non-negative variables. But if we observe that the problem involves variables having unrestricting in-sign, the problem can be converted into an equivalent one involving only non-negative variables.
• Duality theory: – For every linear programming problem, there is another linear programming problem and if the former is referred as primal programming problem, then the latter is called as its dual and vice versa. Duality theory is found to have many applications. The application of duality can be seen in obtaining additional variations in optimal solution when certain changes are effected in the constraint coefficients, resource availabilities and objective function coefficients. This is called as the sensitivity analysis. The detail description and analysis of Biostatics is given by Alternative optimal solutions Assignment Help Online.
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