What is linear programming,it's uses , application and assumptions ?

Linear programming is a mathematical method used to determine the best possible outcome in a given mathematical model for a given set of constraints. It involves optimizing a linear objective function subject to linear equality and inequality constraints.

Uses:
1. Resource allocation: Linear programming can be used to allocate limited resources such as time, money, and materials in the most efficient way possible.
2. Production planning: It can be used to optimize production processes by determining the optimal mix of inputs to maximize output.
3. Transportation and logistics: Linear programming can be used to optimize transportation routes and schedules to minimize costs and maximize efficiency.
4. Financial planning: It can be used to optimize investment portfolios and financial strategies to maximize returns and minimize risks.

Applications:
1. Supply chain management
2. Marketing and advertising
3. Project management
4. Agriculture and farming
5. Healthcare management

Assumptions:
1. Linearity: The objective function and constraints must be linear.
2. Certainty: The values of the coefficients in the objective function and constraints are known with certainty.
3. Non-negativity: The decision variables must be non-negative.
4. Proportionality: The relationship between the decision variables and the objective function is proportional.
5. Additivity: The total contribution of each decision variable to the objective function is the sum of its individual contributions.