A linear program is a type of program which can be referred to as an optimization problem but in a countable many variables having a non geometric region determined by a known number of non geometric equality and inequality constraints.

A linear program can be represented mathematically with some notations, like arithmetic and geometric progression, we can compare them with linear programming, a program can be noted in two forms either geometric or arithmetic. The arithmetic way of coding program can be in these forms.

A linear function of these variables A1,A2,…,An is any function F of the form f(x)=A1X1 +A2X2 +…+AnXn where X is a rational numbe for fixed x belongs to rational number =1…,n.

A linear equality constraints is any form the given equation below

A1X1 +A2X2 +…, +ANXN = α

Where α,X1,X2,…,Xn belongs to the set of rational numbers.

We have many ways of representing linear program, it can be represented by matrix notation and by using vector inequalities

APPLICATIONS OF LINEAR PROGRAMMING

Linear programming can be applied in many ways, linear programming can be used in many fields even in some of our daily activities. Some of its application are given below:

• Resource allocation
• Production scheduling
• Warehousing
• Layout design
• Transportation scheduling
• Facility location
• Supply chain management
• Model selection
• Machine learning
• Compressed sensing
• Flight screw scheduling
• Portfolio optimization
• Cash flow matching
• Currency exchange arbitrage
• Crop scheduling
• Diet balancing
• Parameter estimation

PLASTIC MUGS INDUSTRY

A plastic mug industry is owned by a man, the man wants to optimize their production and maximize his profits. They produce designed mugs. The profit on a case of mugs is $12. This mug are manufactured with a machine called a plastic extruder which feeds on plastic resins. Each case of mugs requires 20 Ibs. Of plastic resins to produce. The daily supply of the plastic resins is limited to at most 1800 pounds. And about 15 cases of the mugs can be produced per hour. At the moment the man wants to limits his work day to 8 hours.

In order for this manufacturer to maximize his profit, he has to model problem as a linear program.

My next publish will be on linear program modeling.