# Types of Linear Programming Problems

Linear programming or linear optimization is a process that 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 linear programming problems (LPP). The LPP’s applications can be found in broad disciplines such as commerce, industry, marketing, distribution, military, economic, business, etc. In this section, we will discuss different types of Linear Programming Problems in detail.

## Different Types of Linear Programming Problems

The different types of linear programming problems are:

• Manufacturing problems
• Diet Problems
• Transportation Problems
• Optimal Assignment Problems

Now, let us discuss all these problems in detail with their constraints and objective function.

### Manufacturing Problems

Manufacturing problems concern maximizing the production rate or net profits of manufactured products, which may be a function of the available workspace, the number of workers, machine hours, packing materials utilized, raw materials required, the product’s market worth, and so on. These are used in the industrial sector and can be used to forecast a company’s potential capital rise over time.

Constraints – Factors such as labour hours, the cost of packing materials, and so on.

The production rate is the objective function.

### Diet Problems

As the name implies, diet problems include maximizing the intake of specific foods high in specific nutrients that can aid in the implementation of a specific diet plan. A diet problem’s purpose is to find a set of foods that will meet a set of daily nutritional requirements for the least amount of money.

Constraints – The nutritional needs that must be met, such as a certain calorie intake or a certain level of sugar or cholesterol in the diet.

The cost of food consumption is the objective function.

### Transportation Problems

The transportation problems are connected to the study of effective transportation routes, or how efficiently products from various sources of production are carried to various markets in such a way that the total transportation cost is minimized. For large organizations with multiple production units and a large customer base, analyzing such issues is critical.

Constraints – The unique patterns of supply and demand.

The transportation cost is the objective function.

### Optimal Assignment Problems

The optimal assignment problems are related to a company’s completion of a specific task/assignment by selecting a specific number of employees to finish the assignment within the required deadline, granted that each individual works on only one job within the assignment. Such issues are seen in event planning and management in large corporations, among other places.

Constraints – The number of employees, the number of hours each employee works, and so on.

The total number of tasks completed is the objective function.

## Types of Linear Programming Problems Summary

 Type of Linear Programming Problem Constraints Objective Function Manufacturing problems Variables such as the cost of packing materials, work hours, and so on Production rate Diet Problems Specified nutritional requirement Cost of food consumption Transportation problems Unique patterns of supply and demand Transportation cost Optimal Assignment problems Work hour of each employee, number of employees, and so on Total number of tasks completed

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