Master Linear Programming Methods using Problem formulation

Linear programming is a technique that can help management in this decision-making process. So linear programming is a mathematical technique for allotting limited resources to a company in an optimal manner.

To effectively apply linear programming methods, one must follow these key steps in problem formulation:

1. Define Decision Variables: Identify the quantities to be determined or controlled. These variables represent decisions or actions that affect the outcome of the problem.

2. Formulate the Objective Function: Create an objective function that expresses the goal in terms of the decision variables. The objective function can be either to maximize or minimize a certain quantity.

3. Set up Constraints: Specify the limitations or restrictions on the decision variables. Constraints can include resource limitations, capacity constraints, demand requirements, and other operational restrictions.

4. Non-negativity Constraints: Declare that decision variables must be non-negative unless explicitly stated otherwise. This ensures that the variables represent feasible quantities or actions.

Some of the examples where linear programming can help find solutions.

1. Diet mix—what do we mean by this? Linear programming can help us find the cheapest combination of foods that will satisfy all our nutritional requirements.

2. Investment decisions: Linear programming can help minimize the risk in your investment portfolio, subject to achieving a certain return.

3. Product mix: Linear programming can help in deciding the product mix to be manufactured in order to generate more profit.

4. Linear programming can also help us in deciding on the advertising that is determining the number of revising units of different realizing media. For example, newspapers, radio, and television are used to ensure maximum exposure.