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Advanced Linear Programming help for students at college level:
Advanced Linear programming is used to find the best or optimal solution to a problem that requires a decision or set of decisions about how best to use a set of limited resources to achieve a state goal of objectives. Linear programming needs that all the mathematical functions in the model be linear functions. A Linear Programming model seeks to maximize or minimize a linear function Advanced Linear Programming to a set of linear constraints.
The steps involved in linear programming are the following:-
The conversion of stated problem into a mathematical model that abstracts all the essential elements of the problem then the exploration of different solutions of the problem and finding out the most suitable or optimum solution.
The linear model comprised of the following components; they are a set of decision variables, an objective function and a set of constraints.
The Importance of Linear Programming are many real world problems lend themselves to linear programming modeling and many real world problems can be approximated by linear models. There are well famous successful applications in manufacturing, marketing, finance, advertising, agriculture. There are efficient solution techniques that solve linear programming models.
The assumptions of linear programming model are that the parameter values are known with certainty. The objective function and constraints exhibit constant returns to scale. There are no interactions between the decision variables.The Continuity assumption: The variables can take on any value within a given feasible range.
Let: X1, X2, X3, ………, Xn = decision variables
Z = Objective function or linear function
Requirement To find the maximization of the linear function Z.
Z = c1X1 + c2X2 + c3X3 + ………+ cnXn …..Eq (1)
Advanced Linear Programming to the constraints where aij, bi, and cj are specified constants.
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- Unsigned variables, SENSITIVITY ANALYSIS, Interpreting the simplex tableau, economic interpretations , Dual prices, Marginal change and return, DUALITY, The dual problem and its motivation, Fundamental Theorem of Duality, Relationships between solutions to the primal and dual problems, Complementary slackness, Interpretations of the Dual problem, Zero-sum games, Integer programming, Assignment problems, Transportation problems.
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