# Linear Programming Problem

Linear Programming is used to find the optimum solution for a given problem, this
might be in the form of profit maximization or lowest cost for a particular mathematical
model. A linear programming model is subject to certain constraints. Linear programming
is also known by its short form LPP (Linear Programming Problem).

**Application of Linear Programming:**

Following are the areas in which Linear Programming is used:

**Portfolio Optimization:**

Linear Programming is increasingly being used by investment companies to determine
the optimal allocation of their assets. Linear programming is used to minimize the
risk for a given investment portfolio for a expected return. The advent of powerful
computers has made solving large investment problems easier taking the guesswork
out of the allocation of assets.

**Military Applications:**

It is used in Military logistics planning. For example: A military logistic problem
would be to determine if different materials can be transported in a tight timeframe
to destinations overseas.

**Crew scheduling:**

Airlines use crew scheduling to optimize the assignment of crews to airlines flight
legs. This is especially useful since the airline crews have strict regulations
on the number of hours they can work. In the airline industry even small savings
add upto millions of dollars, thus increasing profits.

**Other areas where LPP is used:**

- Manufacturing and transportation
- Telecommunications
- Traveling Salesman Problem

**Software Packages Used for Linear Programming Analysis:**

- Excel Solver
- Crystal Ball

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**Topics in Linear Programming:**

- Duality Dual Solutions
- Feasibility Regions
- Graphical Method
- Linear Programming
- Management Science/ Decision Modeling
- Minimize Maximize Optimization
- Objective Functions
- Simplex Method
- Slack variables, basic variables and non-basic variables
- Subject To Constraints
- Transportation Methods

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