Linear Programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
Components of Linear Programming
The basic components of the LP are as follows:
- Decision Variables
- Constraints
- Data
- Objective Functions
Characteristics of Linear Programming
The following are the five characteristics of the linear programming problem:
Constraints – The limitations should be expressed in the mathematical form, regarding the resource.
The constrains in my problem are:
- 1<= All rounders <=4
- 1<= wicket-keepers <=4
- 3 <= Batter <=6
- 3 <= Bowlers <=6
- 4<= Players from team A <=7
- 4<= Players from team B <=7
- Total credit points of the team should not exceed 100
Objective Function – In a problem, the objective function should be specified in a quantitative way.
In my problem we need to maximize the ROI score.
Linearity – The relationship between two or more variables in the function must be linear. It means that the degree of the variable is one.
Finiteness – There should be finite and infinite input and output numbers. In case, if the function has infinite factors, the optimal solution is not feasible.
Non-negativity – The variable value should be positive or zero. It should not be a negative value.
Decision Variables – The decision variable will decide the output. It gives the ultimate solution of the problem. For any problem, the first step is to identify the decision variables.
**In my problem there are 22 decision variables (11 player from team A and 11 player from team B) ** out of these 22, 11 decision variables ahve value 1 and 11 decision variable have value 0. This can also be a constrain.