eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-09-22 2 5 318 323 10.12691/ajams-2-5-4 AJAMS2014254 article OSUJI GEORGE A. 1 OGBONNA CHUKWUDI J. 2 OPARA JUDE judend88@yahoo.com 3 Department of Statistics, Nnamdi Azikiwe University PMB 5025, Awka Anambra State Nigeria Department of Statistics, Federal University of Technology Owerri Nigeria PMB 1526, Owerri Nigeria Department of Statistics, Imo State University PMB 2000, Owerri Nigeria This study is focused on the Application of Transportation Algorithm with volume Discount on distribution cost using Nigerian Bottling Company Plc Owerri Plant. This paper is intended to determine the quantity of Fanta (in crates), Coke (in crates) and Sprite (also in crates) that the Company should distribute in a month in order to minimize transportation cost and maximize profit. A problem of this nature was identified as a Nonlinear Transportation Problem (NTP), formulated in mathematical terms and solved by the Karush-Kuhn-Tucker (KKT) optimality condition for the NTP. A statistical software package was used to obtain the initial basic feasible solution using the Least Cost Method. Thus, analysis revealed that the optimal solution that gave minimum achievable cost of supply was the supply of 5000 crates of Fanta and 6000 crates of the same product to Umuahia market zone and Afikpo respectively. 7000 crates of Coke, 9000 crates and 1000 crates of the same product should be supplied to Orlu, Mbaise, and Afikpo market zones respectively. 6000, and 5000 crates of Sprite should be allocated to Mbaise and Umuahia market zones respectively, at a total cost of N377, 000. http://pubs.sciepub.com/ajams/2/5/4/ajams-2-5-4.pdf Karush-Kuhn-Tucker nonlinear transportation volume discount concave cost