What is linear programming?
What are the components of a linear program?
Answer (2)
Linear programming is a method used to find the best solution to a problem that involves limited resources, like time, money, or materials. It helps you maximize or minimize something, like profit or cost, while following certain rules or limits.Components of a Linear Program (Simple):Decision Variables – What you are trying to find or decide (e.g., how many items to make).Objective Function – What you want to maximize or minimize (e.g., total profit or cost).Constraints – The limits or rules (e.g., budget, time, material limits).Non-negativity Condition – You can't have negative amounts (e.g., you can't make -5 products).
LINEAR PROGRAMMING Linear programming is a math method used to find the best solution to a problem with limited resources. It helps in maximizing or minimizing something — like profit, cost, or time — while following certain rules or limits.Components of a Linear Program: 1. Objective FunctionThis is what you want to maximize or minimize (like profit or cost).Example: Maximize Z = 5x + 7y (where Z is the total profit).2. Decision VariablesThese are the things you want to find or decide (e.g., how many items to make or sell).Example: Let x and y be the number of chairs and tables to make.3. ConstraintsThese are the rules or limits based on resources like time, money, or materials.Example: x + 2y ≤ 100 (material limit) or x ≥ 0, y ≥ 0 (non-negative values)4. Non-negativity RestrictionsThe decision variables can’t be negative, since negative amounts don’t make sense in real-life problems.
