Question

How can linear programming be used in the real world?

Answer 1

The linear programming method is used in the optimization problems in various fields. The optimization is done subject to various constraints. These kinds of optimization problems are faced by the industries providing the services of airlines, medical, agriculture etc.

Complete step by step answer:
In linear programming, we have an optimization problem subjected to linear constraints. This means that we need this method for optimizing something, say, profit, investment, cost etc. The optimization problems are generally related to minimizing the cost, maximizing the profit, minimizing the use of resources etc.
In the optimization problems, we have a linear function, known as the objective function which has to be optimized, subjected to the linear constraints which are expressed as the linear inequalities.
The term linear means that the objective function and the inequalities are the linear functions of the variables. And the term programming refers to the planning of a suitable plan of action, or a program.
Linear programming is widely used in many industries, management science, commerce etc.
For example, in the business and industries linear programming is used in planning, production, transportation etc. for maximizing the profit and minimizing the costs.
The companies associated with the delivery services use linear programming in the scheduling the shipments in the minimum possible time and minimized cost.
Farmers increase their revenue by using linear programming in the determination of the types and the quantity of crops to be grown taking care of the efficient use.

Note: For solving a particular kind of optimization problem by the linear programming method, the graphical method is commonly used. The constraints commonly faced in such problems are basically the resource constraints, storage constraints, investment constraints etc. We must note that all the mathematical relations must be linear otherwise the linear programming method cannot be used.