The assumptions of a linear programming problem include the following:
1. Proportionality: This assumption states that the relationship between the decision variables and the objective function coefficients is linear. This means that a change in the decision variables will result in a proportional change in the objective function value.
2. Additivity: This assumption states that the total contribution of each decision variable to the objective function is the sum of its individual contributions. In other words, the objective function is the sum of the products of decision variables and their coefficients.
3. Certainty: This assumption assumes that all parameters in the linear programming model are known with certainty and are not subject to variability. This includes coefficients of the objective function and constraints, as well as the values of decision variables.
4. Divisibility: This assumption implies that decision variables can take on any non-negative value, including fractional values. This allows for more flexibility in finding an optimal solution to the problem.
5. Linearity: This assumption states that the objective function and all constraints are linear in nature, meaning that they can be represented as linear equations or inequalities. This allows for the use of linear programming techniques to solve the problem.
Overall, these assumptions are essential to the formulation and solution of a linear programming problem, as they help in defining the problem, setting constraints, and finding an optimal solution.
Explain the assumptions of a linear programming problem
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