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Linear Programming : Modeling Example - Coggle Diagram
Linear Programming : Modeling Example
definition
Mathematical method for determining a way to achieve the best outcome in a given mathematical model
Involves optimization of a linear objective function subject to linear equality and inequality constraints
Components of Linear Programming
Decision Variables
Represent the quantities to be determined
Objective Function
Represents the goal to be maximized or minimized
Constraints
Represent limitations or restrictions on decision variables
Modeling Example: Production Planning Problem
Objective
Maximize profit from producing different products
Represents the goal of optimization
Example: Maximizing total profit
problem statement
Example: Maximizing profit from production while considering resource constraints.
decision variable
Quantities to be determined for optimization
Example: Quantity of each product to be manufactured
constrains
Limitations or conditions to be adhered to during optimization
Example: Constraints on available resources like raw materials, labor hours, etc
linear formulation
Expresses the objective function and constraints in a linear mathematical form
Example: Profit = (Profit per unit of product A
Quantity of A) + (Profit per unit of product B
Quantity of B) + ...
solving method
Various algorithms like Simplex Method, Interior-Point Method, etc., used to solve the linear program
Example: Using the Simplex Method to find the optimal solution
optimal solution
Solution that maximizes or minimizes the objective function while satisfying all constraints
Example: Optimal quantities of each product to be manufactured to maximize profit within resource constraints
benefits
Provides a systematic approach to decision-making
Optimizes resource utilization
Offers insights into complex problems
limitations
Assumes linearity in objective function and constraints
May require simplification of real-world scenarios
Sensitivity to changes in parameters