Linear programming or linear optimization is a process which takes into consideration certain linear relationships to obtain the best possible solution to a mathematical model. It includes problems dealing with maximizing profits, minimizing costs, minimal usage of resources, etc. These problems are known as the linear programming problems (LPP). The LPPs find application in broad disciplines such as commerce, industry, marketing, distribution, military, economic, business, etc. In this section, we will discuss different types of LPPs.

### Types of Linear Programming Problems

- Manufacturing problems: These problems involve the production and sale of different products by a company. The production of the products requires a fixed amount of labour force, machine hours, raw material, storage space, etc. Different products are produced so as to satisfy the aforementioned constraints and the investment available. The idea here is to maximize the profit made by the manufacturing company. This accounts for one of the most common type of the linear programming problem.

- Diet problems: Very often the dieticians and nutritionists are required to prepare health and diet charts. The objective of these diet charts is to include all the important kinds of nutrients that are required by the human body to stay healthy. Moreover, the diet should be available at a reasonable cost. Thus, in the diet problems, you are required to include a minimum amount of all important nutrients, thereby minimizing the cost of such a diet plan. Linear programming finds extensive usage in this sector.

- Transportation problems: The products which are produced in factories and manufacturing units are supposed to be transported to the sale points and markets situated at different locations. The idea is to minimize the transporting cost simultaneously ensuring safe and successful transport of the products to the desired locations. These problem statements are examples of the linear programming problems.

To solve examples of the different types of linear programming problems and watch video lessons on them, download Byju’s The Learning App

**Practise This Question**