! EXTENDED ESSAY FINAL VERSION

# ! EXTENDED ESSAY FINAL VERSION - Victoria Shanghai Academy,...

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Victoria Shanghai Academy, Hong Kong Extended Essay Using Linear Programming to maximize profit of the fish-ball stand Au, Cheun Wing Jeffrey Submitted in partial fulfillment of the requirements of the International Baccalaureate Diploma Extended Essay 2009-2011 Subject: Mathematics (Group 5) May 2011 Session Word Count: 3,933 words Centre number: 002634 Candidate number: 002634 - 002

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IB Extended Essay Candidate Name: Jeffrey Au Candidate Number: 002634 – 002 i ABSTRACT: This extended essay is a mathematical research paper that focuses on linear programming and applies it to the real life situation on a fish-ball seller, which provides a detailed case study of a fish-ball stand optimizing profit. This essay will focus on exploring the research question, “how can linear programming be applied to help the fish-ball stand owner decide his quantity of production with the aim of optimizing profit?” This essay examines the concept of linear programming, and analyzes the fish-ball stand situation in terms of profit optimality. The investigation process of both the methodologies of linear programming and the real-life situation of the fish-ball stand went through interviews and discussions, as well as secondary researches like websites, books and videos. Researches are planned and acted upon a regular basis. Linear programming is a mathematical modeling technique that uses real constraints and objectives to find optimal solutions. Converting the unknowns of a real-life situation, such as quantity of production, into decision variables, a linear program can be formed. There are two main ways of solving the problem: the graphical method and the simplex algorithm. Both method aims to improve the objective value of different feasible solutions until optimality is reached. Throughout the investigation process, I have interviewed the owner and found out that he has several constraints that restrict the limitation of his production level. I helped him to analyze the situation with the use of the simplex method and found out that he is not producing at the optimal level. I convinced him to change his production output from 700 fish-balls and 40 pancakes to 340 fish-balls and 85 pancakes, which resulted in the gain of approximately \$72.60 extra profit per day. The hypothetical profit gain the linear program predicted him to obtain is \$90. Word Count: 296
IB Extended Essay Candidate Name: Jeffrey Au Candidate Number: 002634 - 002 ii ACKNOWLEDGEMENTS: I would like to use this opportunity to thank my supervisor, Mr. Slosberg, for devoting his time to guide me through the process of my research and crafting my essay by giving minor, yet helpful advices, even if he has a newborn baby to take care of. I would also like to thank the International Baccalaureate for giving me this excellent opportunity to complete this extended essay and investigate the link between Mathematics, other subjects and my real-life. At last, I would like to thank everyone that has given me support to finish the essay during this seven month‟s time.

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## This note was uploaded on 12/31/2011 for the course PHYS 200 taught by Professor Johnwill during the Spring '11 term at Ave Maria.

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! EXTENDED ESSAY FINAL VERSION - Victoria Shanghai Academy,...

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