# Mathematical Programming

Mathematical programming is a method to find the most optimized solution for mathematical model.

We find the most optimized solution in other fields. For example,
Design of Experiments : To find the most preferred plan of experiment.
Quality Engineering : To find the most stable condition of quality.
Regression Analysis : To find the most likely function.

So, you may have the question, "What is Mathematical Programming?"

I think "Mathematical Programming" is that

• The purpose is to find the most optimized value (maximum, minimum).
• The study is to make method to find the solution.
• Mathematical model in mathematical programming is made in Operations Reserch.

## "Problems" in Mathematical Programming

There are some "problems". Mathematical programming tries to solve those problems. Popular method is Linear Programming

• Production Planning Problem : To find the combination of materials to maximize the benefit
• Transport Problem : To find the route to minimize the cost
• Facility Arranging Problem : To find the arrangement go minimize the cost of transport
• Knapsack Problem : To find the most expensive combination under the condition of weight
• Salesman Problem : To find the shortest route to go around all points

## Linear Programming

If there are several inequality, the range of solution is limited. Linear Programming is the method to find the optimized solution of linear inequalities.