# On Analysis of the Banach’s Fixed Point Iterative Process Using the Simplex Method of Optimization in the Samsung Manufacturing Company Marketing Profit Problem Solution

## Main Article Content

## Abstract

This research aims at generating the topological fixed point iterative scheme for the simplex method of linear programming problem in optimization as exemplified in the optimization of the Samsung manufacturing company marketing profit problem solution displayed in the latter part of section two. Review of basic concepts were discussed in the early part of section two while the model was fully treated in the latter part of section two. Main results concerning the iterative scheme evolved in our discursion in section three.

Keywords:

Linear programming problems, Samsung, simplex method minimization and maximization, sensitivity analysis, contraction, fixed point maps.

## Article Details

How to Cite

*Asian Journal of Pure and Applied Mathematics*,

*2*(2), 19-50. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/847

Section

Review Article

## References

Abul Hassan Siddiqi. Applied functional analysis (Numerical Methods, Wavelet Methods and Image Processing). Marcel Dekker Inc. New York, Basel USA; 2004.

Murray KG. Linear Programming. Wiley New York; 1983.

Schrijver A. Theory of linear and integer programming. Wiley, New York; 1990.

Bender EA. An introduction to mathematical modelling. John Wiley, New York USA; 1997

Brent RP. Algorithms for minimization without derivatives. Prentice-Hall, Eaglewood Cliffs, New York; 1973.

Wosley LA. Integer programming. McGraw-Hill New York; 1983.

Nash SG, Sofar A. Linear and nonlinear programming. McGraw-Hill, New York; 1996.

Fourier R. Linear programming. ORMS Taday. 1997;24:54-67.

Lueaberger DG. Linear and nonlinear programming. 2nd Ed. Addison-Wisley, Menlo Park, CA; 1984.

Vanderbei RJ. Linear programming foundations and economics. Kluwer Academic Publishers Norwell MA; 1999.

Gass SI. An illustrated guide to linear programming. Dover Mineola NY; 1990.

Schittkawski K. Computational mathematical programming. Springer-Verlag, Berlin; 1987.

Beveridge GSG, Schechter R. Optimization theory and Practice. McGraw-Hill, New York; 1970.

Jeter MW. Mathematical programming. Mercel Dekker New York; 1986.

Martin RK. Large scale linear and integer optimization. Kluwer Academic Publishers, Norwell MA; 1999.

Charles Chidume. Geometric properties of banach spaces and nonlinear iterations. Abdusalam International Centre for Theoretical Physics. Trieste, Italy; 2009.

Dantzig GB. Linear Programming and Extensions. Princeton NJ; 1998.

Ioannisk KA. Approximate solution of operator equations. World Scientific Publishing Co. Ptc Ltd. 5 Tola Tuck link Singapore; 2005.

Frigyes Riesz, Belasz-Nagy. Functional analysis. Dover Publications, Inc. New York; 1990.

Fourier R. Software for optimization. ORMS Today. 1999;26:40-44.

Boggs PTR, Byrds H, Schnabel RB. Numerical optimization. SIAM Piladelphia; 1985.

Nocedal J, Wright SJ. Numerical optimization. Springer series in Operations Research New York; 1999.

Hamdry A. Taha. Operation research, an Introduction. 7th ed.; 2005.

Murray KG. Linear Programming. Wiley New York; 1983.

Schrijver A. Theory of linear and integer programming. Wiley, New York; 1990.

Bender EA. An introduction to mathematical modelling. John Wiley, New York USA; 1997

Brent RP. Algorithms for minimization without derivatives. Prentice-Hall, Eaglewood Cliffs, New York; 1973.

Wosley LA. Integer programming. McGraw-Hill New York; 1983.

Nash SG, Sofar A. Linear and nonlinear programming. McGraw-Hill, New York; 1996.

Fourier R. Linear programming. ORMS Taday. 1997;24:54-67.

Lueaberger DG. Linear and nonlinear programming. 2nd Ed. Addison-Wisley, Menlo Park, CA; 1984.

Vanderbei RJ. Linear programming foundations and economics. Kluwer Academic Publishers Norwell MA; 1999.

Gass SI. An illustrated guide to linear programming. Dover Mineola NY; 1990.

Schittkawski K. Computational mathematical programming. Springer-Verlag, Berlin; 1987.

Beveridge GSG, Schechter R. Optimization theory and Practice. McGraw-Hill, New York; 1970.

Jeter MW. Mathematical programming. Mercel Dekker New York; 1986.

Martin RK. Large scale linear and integer optimization. Kluwer Academic Publishers, Norwell MA; 1999.

Charles Chidume. Geometric properties of banach spaces and nonlinear iterations. Abdusalam International Centre for Theoretical Physics. Trieste, Italy; 2009.

Dantzig GB. Linear Programming and Extensions. Princeton NJ; 1998.

Ioannisk KA. Approximate solution of operator equations. World Scientific Publishing Co. Ptc Ltd. 5 Tola Tuck link Singapore; 2005.

Frigyes Riesz, Belasz-Nagy. Functional analysis. Dover Publications, Inc. New York; 1990.

Fourier R. Software for optimization. ORMS Today. 1999;26:40-44.

Boggs PTR, Byrds H, Schnabel RB. Numerical optimization. SIAM Piladelphia; 1985.

Nocedal J, Wright SJ. Numerical optimization. Springer series in Operations Research New York; 1999.

Hamdry A. Taha. Operation research, an Introduction. 7th ed.; 2005.