# 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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