IMPULSIVE SALE-PROFIT MODEL
Keywords:
Impulsive model, Mechanistic, Optimization, Market, sale and Profit
Abstract
This paper considers optimization problems that arise from mathematical economics involving the impulsive sale-profit model of a company producing some items in a mechanically independent non-competitive market situation. The sale and profit profiles of the company are analyzed using a variable allocation of funds for sales promotions, minimizing the cost functional subject to impulsive control and Lyapunov Functional. We formulate the sales projection of the company using the `parasitic control measure' and the impulsive-averaging technique. The result shows that the sale is bounded in a redundant market situation if some sale parameters are finite. The approximate solution and the error of approximation of the model exist.
References
[1] S.O. Ale, B.O. Oyelami.(2000) Impulsive systems and applications. International Journal of Mathematics Education, Science and Technology. 31 , 539 - 544.
[2] D.D. Bainov, D.D. Svetla.(1991) averaging method for neutral type impulsive differential equations with supremums. Annales de la faculte des science de Toulouse. 12.
[3] P. D. Ariel. (1992) A hybrid method for computing the flow of viscoelastic fluids. Int. J. Num. Meth. Fluids. 14, 757-774.
[4] S.A. Bishop, K.S. Eke, H.I. Okagbue.(2021) Advances on Asymptotic Stability of Impulsive Stochastic Evolution Equations. International Journal of Mathematics and Computer Science. 16, 99-109.
[5] S.A. Bishop, A.A. Opanuga, H.I. Okagbue.(2020) Analysis of Stochastic Model of Market Sales Record. International Journal of Supply Chain Management. 9, 30-38
[6] S. Hong, X. Guangming.(2012) Controllability and observability criteria for linear piecewise constant impulsive systems. J. Applied Maths.
[7] V. Lakshimikanthan, D.D. Bainov, P.S. Simeonov.(1989) Theory of Impulsive Differential Equations. World Scientific Publication. Singapore, New Jersey, London, Hong Kong.
[8] S. Leela, A.M. Farzana, Sivasundraham.(1993) Controllability of Impulsive Differential Equation.Journal of Mathematical Analysis and Applications. 177, 24-30.
[9] B.O. Oyelami.(1999) On military models for impulsive reinforcement functions using exclusion and marginalization techniques. Nonlinear Analysis. 35,947- 958.
[10] B.O. Oyelami(2012) -Controllability of Impulsive Systems and application to some physical and biological control systems. International Journal of Differential Equations and Applications. 12, 13-25.
[11] B.O. Oyelami, S.O. Ale, M.S. Sesay.(2002) On existence of solution of impulsive initial and boundary value problems using topological degree approach. Journal of Nigerian Mathematical Society. 21, 13-25.
[12] B.O. Oyelami, S.O. Ale.(2013) Application of Ep stability to financial problems. International Journal of Analysis and Applications, 2, 38-53.
[13] B.O. Oyelami, S.O. Ale.(2012) Impulsive Differential Equations and Applications to Some Models: Theory and Applications. Saarbrucken Lap Lambert Academic Publishing.
[14] B.O. Oyelami.(2012) Studies in impulsive system and applications. Saarbrucken Lap Lambert Academic Publishing.
[15] B.O. Oyelami.(1999) Impulsive Systems and Applications to Some Model. Ph.D. Thesis, Abukakar Tafawa Balewa University, Nigeria.
[16] B.O. Oyelami, S.O. Ale.(2010) On existence of solutions, oscillation and non-oscillation properties of delay equations continuing maximum. Acta Applicandae Mathematical J., 683-701.
[17] B.O. Oyelami, S.A. Bishop.(2020) Impulsive Jump-difusion models for pricing securities. International Journal of Mathematics and Computer Science. 15, 463-483.
[18] P.S. Simeonov, D.D. Bainov.(1993) Theory of Impulsive Differential Equations: Periodic Solutions and Applications. Longman, Essex.
[19] C.Y. Wen, Z.G. Li, Y.C. Soh.(2001) Analysis and Design of Impulsive Control System. IEEE Transaction on Automatic Control. 46.
[20] G. Zhi-Hong, G.H. David, S.S Xuemin.(2005) IEEE Transaction on Automatic Control. 50.
[21] R. Sakthivel, J.N. Juan, Mahmudov.(2010) Approximate controllability of nonlinear differential and stochastic with unbounded delay Taiwanese J.Math. 14, 1777-1797.
[2] D.D. Bainov, D.D. Svetla.(1991) averaging method for neutral type impulsive differential equations with supremums. Annales de la faculte des science de Toulouse. 12.
[3] P. D. Ariel. (1992) A hybrid method for computing the flow of viscoelastic fluids. Int. J. Num. Meth. Fluids. 14, 757-774.
[4] S.A. Bishop, K.S. Eke, H.I. Okagbue.(2021) Advances on Asymptotic Stability of Impulsive Stochastic Evolution Equations. International Journal of Mathematics and Computer Science. 16, 99-109.
[5] S.A. Bishop, A.A. Opanuga, H.I. Okagbue.(2020) Analysis of Stochastic Model of Market Sales Record. International Journal of Supply Chain Management. 9, 30-38
[6] S. Hong, X. Guangming.(2012) Controllability and observability criteria for linear piecewise constant impulsive systems. J. Applied Maths.
[7] V. Lakshimikanthan, D.D. Bainov, P.S. Simeonov.(1989) Theory of Impulsive Differential Equations. World Scientific Publication. Singapore, New Jersey, London, Hong Kong.
[8] S. Leela, A.M. Farzana, Sivasundraham.(1993) Controllability of Impulsive Differential Equation.Journal of Mathematical Analysis and Applications. 177, 24-30.
[9] B.O. Oyelami.(1999) On military models for impulsive reinforcement functions using exclusion and marginalization techniques. Nonlinear Analysis. 35,947- 958.
[10] B.O. Oyelami(2012) -Controllability of Impulsive Systems and application to some physical and biological control systems. International Journal of Differential Equations and Applications. 12, 13-25.
[11] B.O. Oyelami, S.O. Ale, M.S. Sesay.(2002) On existence of solution of impulsive initial and boundary value problems using topological degree approach. Journal of Nigerian Mathematical Society. 21, 13-25.
[12] B.O. Oyelami, S.O. Ale.(2013) Application of Ep stability to financial problems. International Journal of Analysis and Applications, 2, 38-53.
[13] B.O. Oyelami, S.O. Ale.(2012) Impulsive Differential Equations and Applications to Some Models: Theory and Applications. Saarbrucken Lap Lambert Academic Publishing.
[14] B.O. Oyelami.(2012) Studies in impulsive system and applications. Saarbrucken Lap Lambert Academic Publishing.
[15] B.O. Oyelami.(1999) Impulsive Systems and Applications to Some Model. Ph.D. Thesis, Abukakar Tafawa Balewa University, Nigeria.
[16] B.O. Oyelami, S.O. Ale.(2010) On existence of solutions, oscillation and non-oscillation properties of delay equations continuing maximum. Acta Applicandae Mathematical J., 683-701.
[17] B.O. Oyelami, S.A. Bishop.(2020) Impulsive Jump-difusion models for pricing securities. International Journal of Mathematics and Computer Science. 15, 463-483.
[18] P.S. Simeonov, D.D. Bainov.(1993) Theory of Impulsive Differential Equations: Periodic Solutions and Applications. Longman, Essex.
[19] C.Y. Wen, Z.G. Li, Y.C. Soh.(2001) Analysis and Design of Impulsive Control System. IEEE Transaction on Automatic Control. 46.
[20] G. Zhi-Hong, G.H. David, S.S Xuemin.(2005) IEEE Transaction on Automatic Control. 50.
[21] R. Sakthivel, J.N. Juan, Mahmudov.(2010) Approximate controllability of nonlinear differential and stochastic with unbounded delay Taiwanese J.Math. 14, 1777-1797.
Published
2024-07-14
How to Cite
Oyelami, B. O., & Bishop, S. A. (2024). IMPULSIVE SALE-PROFIT MODEL. Unilag Journal of Mathematics and Applications, 3, 71-80. Retrieved from http://lagjma.unilag.edu.ng/article/view/2145
Issue
Section
Articles
Copyright (c) 2023 Benjamin Oyediran Oyelami, Sheila Amina Bishop
This work is licensed under a Creative Commons Attribution 4.0 International License.
