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Linear Programming And Mathematical Optimization

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Linear programming which is also known as “Linear Optimization” is a way to achieve best outcomes in a Mathematical Model using different linear solutions .Linear Programming is a special case of Mathematical Optimization .Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries.
The method of Linear Programming was originally developed by American mathematicians between 1945 and 1955 to solve problems arising in economic planning ad industries .The problems involve constraints, quantity of raw material available in the industry. Linear Programming problems are generally solved by graphical representation if …show more content…
Formulate the above given LPP.
SOLUTION:
Let us define as: x = no of TYPE A sheds produced everyday y = no of TYPE B sheds produced everyday
CONSTRAINTS:
Machine time: 2x+3y=0, y>=0.
PROFIT :
P= 60x+84y
So basically the linear programming problem is to maximize P = 60x + 84y in accordance to the conditions given above .In this way , we solve a LPP . we can also represent it Graphically .
Linear Programming is Generalization of Linear Algebra; it is capable in handling a variety of problems. The reason for this great versatility is the ease at which constraints can be incorporated in the model.
FORMULATION OF LPP:
Linear programming is a mathematical technique for analysis and optimum allocation of limited resources present to us. Optimum Allocation here refers to how limited or scarce resources are used so as to give us the maximum profit, limited resources like labour, machines, money etc.
Structure of Linear Programming Model:
Generally, a Linear programming method has three necessary components:
1- The variables and their relationship
2- The Objective function
3- The

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