This larger superset of linear programming applications is referred to as mathematical programming or optimisation because it seeks to maximise (or minimise) a given objective …
In this study, we develop and apply a user friendly interface that provides solutions to linear programming (LP) problems. Specifically given an objective function that is subject to a set of linear constraints, which arise in a variety of LP-type problems, the interface was used to secure optimal solutions. A more restricted type of LP problem-the travelling salesman problem (TSP)-which is a special type of integer linear programming (ILP) problem whose objective is to discover an optimal tour that minimises the distance travelled by a salesman was solved with the interface. The paper also presents graphical solutions for the TSP with instances of up to 5 cities in a given tour. Examples are presented that illustrate the adaptive qualities of the TSP to variability of the values in the distance matrix. Ultimately it is hoped that the LP and TSP user interface will serve as a learning tool for mathematical programming students to enable them visualise solutions to esoteric LPs, ILPs and TSPs. Lecturers and other educators may also take advantage of the flexibility of the interface in their work since no experience is required to use it. The study proposes a number of extensions to the interface which other professionals and researchers could undertake. I would like to thank Professor Astolfi for his sustained encouragement throughout the conduct of this study. His guidance and support during the year were invaluable and motivated me to proceed further than I initially thought possible with this paper. I am also deeply indebted to Dr. Rustem who kindly emailed his lecture notes on Linear programming and Integer Linear Programming. In addition I would like to thank Dr. Bemporad from Sienna for promptly emailing his Hybrid Optimisation toolbox which saved much effort and time during the development of the TSP user interface. I would also like to thank Big Pete for tirelessly proof reading this paper and Dr. Allwright for being the voice of logic when debugging difficulties arose. Finally, I am most grateful to my parents and family for having invested so much time and energy to see that I reached my desired goal and steering me selflessly to continuously higher levels of personal achievement…

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