## STUDY ON ALLOCATION OF PRODUCTION RESOURCES FOR AN OPTIMAL PROFIT MAKING

Published: 2022-12-20

Page: 13-22

P. N. EZRA *

Department of Statistics, University of Nigeria, Nsukka, Nigeria.

E. O. OSSAI

Department of Statistics, University of Nigeria, Nsukka, Nigeria.

F. O. OHANUBA

Department of Statistics, University of Nigeria, Nsukka, Nigeria.

M. N. EZE

Department of Statistics, University of Nigeria, Nsukka, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

In this study, the limited resources of a production company are maximally allocated for the production of cake of different sizes for optimal profit making. The datasets used were collected on the profit made from four different sizes of the cake and on the available production resources of the company. The profits made from the various cake sizes form the objective function coefficients; the measurements of the various resources used for the production of the different sizes of the cake form the coefficients in the constraint equations while the total available resource quantities form the right hand sides of the constraint equations. The resultant linear programming problem was solved and the result showed the various quantities of the cake sizes that should be produced so as to make an optimal profit. Sensitivity analysis was carried out to determine the robustness of the formulated model.

Keywords: Linear programming, objective function, sensitivity analysis, optimal solution

#### How to Cite

EZRA, P. N., OSSAI, E. O., OHANUBA, F. O., & EZE, M. N. (2022). STUDY ON ALLOCATION OF PRODUCTION RESOURCES FOR AN OPTIMAL PROFIT MAKING. Asian Journal of Mathematics and Computer Research, 29(4), 13–22. https://doi.org/10.56557/ajomcor/2022/v29i47988

### References

Mahesh SN. Profit maximization in bakery by optimal allocation of raw materials; 2020.

Available:http://aegaeum.com/ 8(5), 391-393

Mustafa A, Sayegh M, Rasheed S. Application of linear programming for optimal investments in software company. Open Journal of Applied Sciences. 2021;11(10):1092-1101.

Rama S, Srividya S, Deepa B. A linear programming approach for optimal scheduling of workers in a transport corporation. International Journal of Engineering Trends and Technology (IJETT). 2017;45(10): 482-487.

Oluwaseyi KO, Atsegameh E, Olaoluwa OE. Profit maximization in a product-mix bakery using linear programming technique. Journal of Investment and Management. 2020;9(1):27-30.

Kumar A, Kaur J. General form of linear programming problems with fuzzy parameters. Journal of Applied Research and Technolog (JART). 2013;11(5):629-635.

Kumar PP, Vinodkumar O, Yugandhar T. An optimization technique on the managerial decision making. International Journal of Mechanica land Production Engineering Research and Development. 2018;8(6): 507-516.

Lokhande K, Khot PG, Khobragade NW. Alternative approach to the optimum solution of linear programming problem. International Journal of Lates Technology in Engineering, Management and Applied Science. 2017;6(6):61-68.

Shaheen S, Ahmad T. Linear programming based optimal based resource utilization for manufacturing of electronic toys. International Research Journal of Engineering and Technology (IRJET). 2015;2(1):261-264.

Woubante GW. The optimization problem of the product mix and linear programming applications: A case study in the apparel industry. Open science Journal. 2017;2(2):1-11.

Oyekan EA, Temisan GO. Application of linear programming to profit maximization of Johnsons Nigerian Ltd., bakery division. Journal of Advances in Mathematical & Computational Sciences. 2019;7(1):11-20.

Sumathi P. A new approach to solve linear programming problem with intercept values. Journal of Information and Optimization Sciences. 2016;37(4):495-510.

Zaman H, Rizwan F, Muhammad BT, Syed U, Naeem U, Sehrish K. Application of linear programming for profit maximization: A case study of paints company, Pakistan. International Journal of Management Sciences and Business Research. 2016;5(12):144-151.

Akpan NP, Iwok IA. Application of linear programming for optimal use of raw materials in bakery. International Journal of Mathematics and Statistics Invention. 2016;4(8):51-57.

Ammar EE, Emsimir AA. A mathematical model for solving integer linear programming problem. African Journal of Mathematics and Computer Science Research. 2020;13(1):39-50.

Charnes A, Cooper WW. Management models and industrial applications of linear programming. John Wiley and Sons, New York; 1961.

Dantzig GB. Linear programming and extension, Princeton, New Jersey, Princeton University Press; 1947.

Anieting AE, Ezugwu VO, Ologun S. Application of linear programming technique in the determination of optimum production capacity. IOSR Journal of Mathematics (IOSR-JM). 2013;5(6):62-65.

Balogun OS, Jolayemi ET, Akingbade TJ, Muazu HG. Use of linear programming for optimal production in a production line in coca-cola bottling company. International Journal of Engineering Research and Applications. 2012;2(5):2004-2007.

Felix M. Incorporating crop rotational requirements in a linear programming model: A case study of rural farmers in Bindura, Zimbabwe. International Researchers. 2013;2(2):58-61.

Ezema BI, Amakon U. Optimizing profit with linear programming model: A focus on golden plastic industry limited Enugu Nigeria. Interdisciplinary Journal of Research Business. 2012;2(2):37-49.

Ezra PN, Oladugba AV, Ohanuba FO, Igwe NO, Okonta CA. Application of linear programming on the profit maximization of Nigerian Bottling Company. American Journal of Operational Research. 2020;10(2):39-43.