This study tries to factor O.R (optimization) into entrepreneurship for the purpose of profit maximization. Primary data from an entrepreneur was collected. The data analysis, optimization application software (TORA) was used. The optimal solution were X2 (moccasin) = 9.09 and X3 (Italian) = 6.36 for a profit of Zmax = N2836.36 and it was concluded that the entrepreneur (shoe producer) should produce 9.09 units of moccasin and 6.36 units of Italian shoes for a daily profit of N2836.36 and that they should not produce X2 (paddock) and X4 (cover front) types of shoes in the face of the constraints posed by the operating environment. Keywords: Entrepreneur, optimization, profit maximization.

Steve .C, Nwankwo

English

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Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  78 Optimization of Entrepreneurship by the Application of Linear Programming Technique Nwankwo Steve .C School of Science And Industrial Technology Department of Statistics, Abia State Polytechnic, Aba P.M.B 7166, Nigeria. Email:stevenwankwo@yahoo.com; phone No: 08056330895 ABSTRACT This study tries to factor O.R (optimization) into entrepreneurship for the purpose of profit maximization. Primary data from an entrepreneur was collected. The data analysis, optimization application software (TORA) was used. The optimal solution were X2 (moccasin) = 9.09 and X3 (Italian) = 6.36 for a profit of Zmax = N2836.36 and it was concluded that the entrepreneur (shoe producer) should produce 9.09 units of moccasin and 6.36 units of Italian shoes for a daily profit of N2836.36 and that they should not produce X2 (paddock) and X4 (cover front) types of shoes in the face of the constraints posed by the operating environment. Keywords: Entrepreneur, optimization, profit maximization.    1.0 INTRODUCTION An unemployed youth is a trained soldier for destruction. Any nation where unemployment is on the increase, no doubt, crime will also be on the increase because unemployment and crime are directly proportional to each other. The Nigerian government has gone a long way in tackling this problem by making entrepreneurship compulsory in schools. But this is not enough as no business runs without profit maximization as a goal. This is why optimization has to be factored into entrepreneurship to avoid wasted investments. Therefore, this work is promising its quota in boosting entrepreneurship through optimization. Any business, anywhere in the world has common problem which is limitation or restriction. The inability to manage these restrictions can cause liquidation. And one may begin to wonder what are these limitations and how do the restriction bring about liquidation. This work seeks to encourage entrepreneurs by helping to maximize their profit in the face of constraints, to avoid losses. To help the government to fight unemployment through entrepreneurship development and encouragement, to the youths. Information on the number of products produced by an entrepreneur, their hours, which has to do with time taken to produce a product as well as the length of time staked per day, cost price, profit per day. All this together will help to estimate the best possible combination of this man-hour so as to make maximum profit and minimize losses. Those information, together will help minimum cost as well as knowing the product that requires most time or working hour, so as to make maximum profit and reduce wastage materials and human resources. This paper is organized into five sections namely Introduction, Literature Review, Methodology, Data Analysis and Conclusion. 2.0 REVIEW OF RELATED LITERATURE Entrepreneurship is a French word used broadly to connote, innovative modern industrial business leadership. It originated from a French word “entreprendre” which means “undertake”. The name is as a result of the fact that the entreprendre can undertake the risk of the enterprise. Mr. Richard Cantillon, an Irish man, who was living in France, then first used the term entrepreneurship in the early 18th century. George A.A. (2007) says entrepreneurship is concerned with innovation and management. He sees entrepreneurship as either a creative innovator that is creating something new that is capable of satisfying consumer’s wants or an adaptive innovator who can modify an existing or similar products or services for better performance while also engaged in managerial activities of planning, controlling, organizing, directing and co-ordinating his business to achieve the objectives of the enterprise.  Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  79 This research work seeks to factor optimization into entrepreneurship to maximize profit. Optimization in operations research has a single goal of maximization of profit or minimization of losses. Gupta and Hira (2010) define operations research as the application of scientific methods and techniques to decision-making problems. Handy A.T. (2003) define operations research as the attack of modern science on complex problems arising in the direction and management of large systems of men, machine, materials and money, industry, business, government and defence. Its distinctive approach is to develop a scientific model of the system, incorporating measurements of factors such as change and risk with which to predict and compare the outcomes of alternatives, strategies or controls. The purpose is to help management determine its policy and actions scientifically. There is no doubt that its application into entrepreneurship will be an indispensible approach. 3.0 METHODOLOGY The data used in the analysis of this work was collected from an entrepreneur who specializes in making shoes at Ariaria Aba. He was interviewed. We recorded the stages, and time taken to produce his shoes named as; Moccasin, Paddock, Italian and coverfront. The data collected summarized the current state of activities. The production process takes a repetitive approach unless a new product line is introduced or another worker employed. The observation process was carried out for two weeks each in the month of July and August so as to know if there will be any deviation in the mode of operation but everything proved to be the same since the process was repetitive enough. The recorded information from the entrepreneur is shown on the table at the Appendix. 4.0 Data Analysis  A linear programming model for the maximization of objective function type can be stated mathematically as follows: Maximize Z = C1X1 + C2X1 + C3X3 + … + CnXn Subject to                                                                                              And                     Where  i. X1, X2, …, Xn are decision variables to be maximize they are representing the entrepreneurs products i.e. X1 = Moccasin,  X2 = Paddock, X3 = Italian and X4 = coverfront. ii. C1, C2, …, Cn are the unit profit of the different activities.  iii. aij’s are the input-output coefficients or the quantity of a resource i required a produce a unit of an activity j. For example, it takes 35 minutes at the first stage of moccasin production; the aij in this case is 35 (see appendix). iv. b1, b2, …, bm are the quantities of resources or their restrictions available where i = 1,2, …, m. v. Z = the objective function to be maximized. The maximization of Z is carried out so that the m constraints are satisfied.   Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  80 TORA MOMENT OPTIMIZATION SOFTWARE TORA optimization system is a window-based software designed for use in operation research. It was used to solve and analysis the LP model in appendix. TORA is totally self-contained, in that all the instructions needed to drive the software are presented by menu, command buttons, check boxes etc. To use TORA with the Reddy Mikks model, enter the model, from the solve/modify menu, select solve – Algebraic – iterations – all – slack. Next, click GOTO output screen.  You can generate one or all iterations by clicking next iteration or all iterations. If you opt to generate the iterations one at a time, you can interactively specify the entering and leaving variables by checking the headings of their corresponding column and row. If your selections are correct, the column turns green and the row turns red. Else, an error message will be posted. DATA ANALYSIS USING OPTIMIZATION SOFTWARE (TORA MOMENT) TORA Optimization System Windows@version 2.00 Copyright © 2000-2007 Hamdy A. Taha. All Rights Reserved Thursday, September 19, 2013 10.27  LINEAR PROGRAM – ORIGINAL DATA Title: Reddy mikks model   Moccas Paddoc  Italia  Coverf          x1               x2            x3        x4 Maximize 200.00  250.00  160.00  150.00 Subject to (1)   35.00  40.00  25.00  20.00  <=  500.00 (2)  15.00  20.00  25.00  30.00  <= 540.00 (3)  30.00  50.00  20.00  25.00  <= 400.00 (4)  25.00  20.00  35.00  30.00  <= 450.00  Lower Bound  0.00   0.00    0.00   0.00 Upper Bound 35.00  50.00  35.00  30.00 Unrestr’d (y/n)?         n          n         n         n       Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  81                 SIMPLEX TABLEAUS – (Starting All-Slack Method)  Title: Reddy mikks model  Iteration 1 Moccas  Paddoc  Italia  Coverf         Basic        x1                x2         x3        x4  sx5  sx6      Z(max) -200.00  -250.00        -160.00          -150.00  0.00  0.00 Sx5    35.00     40.00  25.00    20.00  1.00  0.00 Sx6    15.00     20.00  25.00    30.00  0.00  1.00 Sx7    30.00     50.00  20.00    25.00  0.00  0.00 Sx8    25.00     20.00  35.00    30.00  0.00  0.00        Lower Bound       0.00       0.00        0.00       0.00        Upper Bound     35.00  50.00  35.00    30.00 Unrestr’d(y/n)?          n                  n                   n          n   Basic       sx7  sx8        Solution         Z(max)     0.00      0.00        0.00  Sx5     0.00      0.00    500.00  Sx6     0.00      0.00    540.00  Sx7     1.00      0.00    400.00  Sx8     0.00      1.00    450.00   Iteration 2 Moccas  Paddoc  Italia  Coverf        Basic         x1                x2         x3        x4  sx5  sx6    Z (max) -50.00      0.00  -60.00  -25.00  0.00  0.00  Sx5  11.00      0.00       9.00     0.00  1.00  0.00           Sx6    3.00      0.00   17.00  20.00  0.00  1.00  X2    0.60      1.00      0.40    0.50  0.00  0.00          Sx8  13.00      0.00  27.00  20.00  0.00  0.00 Lower Bound   0.00      0.00    0.00    0.00   Upper Bound 35.00    50.00  35.00  30.00 Unrest’d(y/n)?       n          n        n        n    Basic       sx7  sx8        Solution         Z(max)     5.00      0.00   2000.00  Sx5     0.00      0.00     180.00  Sx6     0.00      0.00     380.00    X2     1.00      0.00         8.00  Sx8     0.00      1.00     290.00      Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  82  Iteration 3 Moccas  Paddoc  Italia  Coverf        Basic         x1                x2          x3        x4  sx5  sx6    Z (max) -21.11      0.00             0.00  19.44  0.00  0.00           Sx5    6.67      0.00     0.00   -6.67  1.00  0.00           Sx6    -5.19      0.00             0.00    7.41  0.00  1.00  X2    0.41      1.00             0.00    0.20  0.00  0.00            X3    0.48      0.00   1.00    0.74  0.00  0.00  Lower Bound    0.00      0.00    0.00    0.00    Upper Bound 35.00    50.00  35.00  30.00 Unrest’d(y/n)?       n          n        n        n     Basic       sx7  sx8        Solution         Z(max)     4.11      2.22   2644.44  Sx5     -0.67  -0.33       83.33  Sx6     -0.15   -0.63     197.41    x2     0.03      -0.01         3.70    x3     -0.01   0.04       10.74     Iteration 4 Moccas  Paddoc  Italia  Coverf        Basic         x1                x2          x3        x4  sx5  sx6    Z (max)     0.00     51.82             0.00  30.00  0.00  0.00           Sx5     0.00   -16.36     0.00            -10.00  1.00  0.00           Sx6     0.00     12.73             0.00   10.00  0.00  1.00  X1     1.00      2.45             0.00     0.50  0.00  0.00            X3     0.00     -1.13   1.00     0.50  0.00  0.00 Lower Bound     0.00      0.00    0.00     0.00   Upper Bound   35.00    50.00  35.00   30.00 Unrest’d(y/n)?         n          n        n         n    Basic       sx7  sx8         Solution         Z(max)     4.11      2.22   2644.44  Sx5     -0.67  -0.33       83.33  Sx6     -0.15   -0.63     197.41    x1     0.03      -0.01         3.70    x3     -0.01   0.04       10.74     5.0 CONCLUSION This research work has been able to analyze the current activity of an entrepreneur using linear programming technique. From the analysis and optimality tests carried out using TORA software, it is observed that an optimal solution has been attained at  X1 = 9.09, X3 = 6.363 and Zmax = 2836.08 while X2 and X4 did not appear in the final solution. It is worthy of note that X1, X2, X3 and X4 are the decision variables which represent shoe types, Moccasin, Paddock, Italian and coverfront. Also, the slack variables, S1, S2, S3 and S4 where not taking into consideration in the final result as they have no economic value. From the above findings, for the entrepreneur to make a maximum profit of N2836.36, the should produce 9.09 units of moccasin and 6.36 units of Italian shoes and stop the production of paddock and coverfront as they (paddock and coverfront) do not contribute to the maximum profit the entrepreneur makes in the face of the constraints they operate upon. This conclusion holds for the current activity in the entrepreneur’s office. If more products are introduced by this entrepreneur, no doubt, the result will be violated but for this four products (Maccasin, paddock, Italian, coverfront), and their profits together with constraints and available resource which are present in the data collected. Mathematical Theory and Modeling                                                                                                                                                  www.iiste.org ISSN 2224-5804 (Paper)    ISSN 2225-0522 (Online) Vol.4, No.5, 2014  83 Based on the analysis made and the conclusion drawn, the entrepreneur is advice to stop producing paddock and coverfront and produce 9.09 units of moccasin and 6.36 units of Italian shoes per day for them make a maximum profit of N2836.36 per day.  This method of profit maximization should be adopted by other entrepreneurs in their business in order to escape liquidation and frustration. Nigerian graduates should embrace this entrepreneurial development and go into it, so as to reduce unemployment. APPENDIX The four shoes and the daily capacity of the four stages are given in the table below. Source: An Entrepreneur (Shoes producer) Ariaria Aba  Time per unit (minutes) of production  Stages Moccasin Paddock Italian Coverfront Capacity per stage (minute/day) 1 35 40 25 20 500 2 15 20 25 30 540 3 30 50 20 25 400 4 25 20 35 30 450 Profit(N) 200 250 160 150   The linear programming for maximization is  Maximize (Z) = N200X1 + N250X2 + N160X3 + N150X4 Subject to 35x1 + 40x2 + 25x3 + 20x4  500 15x1 + 20x2 + 25x3 + 30x4  540 30x1 + 50x2 + 20x3 + 25x4  400 25x1 + 20x2 + 35x3 + 30x4  450 X1, X2, X3, X4     REFERENCE George A. Anugwon (2007). Entrepreneurship in Nigeria, Rhyce Kerex Publishers, Enugu Gupta P.K and Hira D.S (2010). Operations Research, Schand and company Ltd, New Dehi Handy A. Taha (2003) Operations Research an Introduction, Seveth Edition, Prentice-Hall India J.K. Olayemi and C.E. Onyenwaku (1999). Quantitative Methods for Business Decision, Bosude Printers Ltd, Ibadan   The IISTE is a pioneer in the Open-Access hosting service and academic event management.  The aim of the firm is Accelerating Global Knowledge Sharing.  More information about the firm can be found on the homepage:  http://www.iiste.org  CALL FOR JOURNAL PAPERS There are more than 30 peer-reviewed academic journals hosted under the hosting platform.   Prospective authors of journals can find the submission instruction on the following page: http://www.iiste.org/journals/  All the journals articles are available online to the readers all over the world without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself.  Paper version of the journals is also available upon request of readers and authors.   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Optimization of Entrepreneurship by the Application of Linear Programming Technique

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Optimization of Entrepreneurship by the Application of Linear Programming Technique

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