Question

What are the assumptions and limitations of linear programming?

Answer 1

Hint: Here the question is related to the Linear Programming Problem. The question is a direct question, here we have to write the limitations and assumptions of the linear programming problem. The meaning of limitations is the restricted thing and the assumptions means something is true or will happen. So below points represent the limitations of the Linear programming Problem.

Complete answer:
Linear programming is a method for determining optimum values of a linear function subject to constraints expressed as linear equations or inequalities.
The limitations of Linear Programming problem is given as follows:
1.It deals with optimizing a single objective. In practice, a number of objectives may be there.
2.The assumption that input and output variables are directly proportional is not strictly true. Economics of scale usually ensure that the more you produce, the less the average cost.
3.The linearity of variables assumes that resources required for multiple activities are the sum total of resources required for individual activities. However, synergies of product mix usually mean that the requirement is less than the sum.
I4.n practice, many decision variables assume integral values, e.g., number of workers. L.P deals with variables having continuous values.
The assumptions of linear programming is given as follows:
1.Proportionality: The basic assumption underlying the linear programming is that any change in the constraint inequalities will have a proportional change in the objective function.
2.Additivity: The assumption of additivity asserts that the total profit of the objective function is determined by the sum of profit contributed by each product separately. Similarly, the total amount of resources used is determined by the sum of resources used by each product separately.
3.Continuity: Another assumption of linear programming is that the decision variables are continuous. This means a combination of outputs can be used with the fractional values along with the integer values.
4.Certainty: Another underlying assumption of linear programming is certainty, i.e. the parameters of objective function coefficients and the coefficients of constraint inequalities is known with certainty. Such as profit per unit of product, availability of material per unit, requirement of material per unit are known and are given in the linear programming problem.
5.Finite Choices: This assumption implies that the decision maker has certain choices, and the decision variables assume non-negative values. The non-negative assumption is true in the sense, the output in the production problem cannot be negative. Thus, this assumption is considered feasible.

Note:
By using the Linear Programming problem, we can solve the problems related to Manufacturing problems, Diet problems and Transportation problems.