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Analysis Of The Linear Model Using Microsoft Office Excel 's Solver

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1. Introduction
It is acknowledged that real-world situations could be represented by well structured and formulated Linear Programming models. These mathematical tools contribute significantly to business activities and can be used to tackle problems that constantly arise.
Franco Sounds is a company specialised in manufacturing Hi-Fi Amplifiers of top quality and its main goal, at the moment, is to minimise its overall production and transportation cost.
This report presents a quantitative analysis which has been conducted in order to fulfil the company’s goal. The primary purpose of it is to provide the clients with the best recommendations drawn from the model’s formulation and solution as well as to underline all the crucial assumptions.
The following objectives had been considered:
a. A formulation of the appropriate linear programming model for the optimal solution
b. An analysis and interpretation of the linear model using Microsoft Office Excel’s Solver.

2. Definition of the problem
In three cities of Europe, such as Porto, Bratislava and Vilnius, Hi-Fi Amplifiers, are produced by Franco Sound. Each plant is respectively capacitated with 2500, 1500 and 1000 units per month. The company’s markets are located in ten different European cities as well, each of which has a demand per month. (Table 1 – Appendix A) Its products are transported by road and ferry, via the shortest route, and the unit transportation cost, from each city to each destination is £0.01 per/km.
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