Knapsack algorithm a case study of garden city radio (a local radio station in Kumasi)

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The knapsack or rucksack problem is a problem in combinatorial optimization. It derives its name from the maximization problem of the best choice of essentials that can fit into one bag to be carried on a trip. Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than a given limit and the total value is as large as possible. The decision problem of the knapsack problem is the question "can a value of at least V be achieved without exceeding the weight W?" The problem often arises in resource allocation with constraints. The practice of selecting commercials to be played on air from a pile of commercials in most radio stations to generate the maximum revenue given a fixed time is a clear case of Knapsack Problem. In this project, we shall explore ways of effectively and efficiently selecting commercials from a pile of commercials within a fixed time to achieve optimal use of air time in order to maximize space and airtime in the FM stations in Ghana, using knapsack algorithm and also to develop a software for the knapsack algorithm using Visual Basic dot NET, which can be used by any researcher or radio station. The software will also be modeled to solve many industrial problems: capital budgeting, cargo loading, cutting stock, to mention the most classical applications. Our project will also serve as reference material in the libraries and the internet for students who wish to undertake research into the piled-up problems of commercials and programmes. The project may also serve as a guide for policy makers and the general public. In this project, different algorithm used to solve Knapsack problem is briefly discussed but the Heuristic Scheme will be used to solve the Knapsack Problem.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology In partial fulfillment of the requirement for the degree of Master oF Science.