Abstract
Linear programming (LP) is an important part of applied mathematics. This method has found its applications to important areas of product mix, blending, and diet problems. Steel, chemical, food processing industries and Oil refineries industry are also using LP with considerable success. But in practical LP can be very large. In this paper, our intent is to formulate an LP model of some large-scale real-life-oriented problems and to apply computer techniques for solving these problems. Starting with the graphical procedure which provides an ample amount of understanding into some fundamental concepts, the simple procedure of solving LP problems is developed. Finally, a special class of LP problem, namely Transportation is taken up and solved. We also solved the simplex system by using FORTRAN programming.
Highlights
Linear programming (LP) is called linear optimization it’s applies to optimization models inside of which the objective and constraint functions are strictly linear
In this paper, we have formulated mathematical programming model of sizeable real life problem and we solved these problems with Mathematica and FORTRAN code
We solved some problem by hand calculation and again those problem is solved by FORTRAN program
Summary
Linear programming (LP) is called linear optimization it’s applies to optimization models inside of which the objective and constraint functions are strictly linear. If all of the portions of the non-general variables in the targeted function equation are less than or equal to 0 (zero) at some point, an optimal result for the real model has been reached. That’s, if all coefficients of the non-basic variables in the targeted function equation are bigger than or equal to 0 at some given point, a best result for the real model has been reached. 3) If all of the slack, surplus, and non-natural are zero when an classical solution of the equivalent model is reached, all of the constraints in the real model are strict “equivalence” for the values of the variables that optimize the targeted function. FORTRAN Program for solving simplex method In this paper, our intent is to formulate linear programming model of some large-scale real life oriented problems and to apply computer program for solving these.
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