INSTRUCTIONS

1) Carry out a prior analysis of the information presented, indicating your assumptions and any other type of preliminary information that you consider important for the resolution and understanding of your proposed solution. 2) Correctly pose each case as an operations research model, following the technique used for each situation (Markov Chains, Queuing Theory, Waiting Models) Do not limit yourself to just listing the information, but you are expected to explain in detail each of the elements that make up the approach. 3) Use an appropriate computer program to solve the problem, addressing each of the scenarios (if any) requested. Please present this solution model in an attachment and Excel. 4) Present the solution or solutions obtained, clearly explaining its interpretation and the impact that This solution will have in the original conditions of the case. 5) Present a conclusion regarding the case analyzed that synthesizes your findings during the process of presenting and resolving the case. Recommendations that go beyond the simple numerical solution will be appreciated. 6) At the end, a conclusion or reflection on the problem must be presented, indicating which parts were problematic, what techniques you used and finally, what you observed during the resolution process.

Case 1

Davidson Manufacturing Company is planning an extensive advertising campaign to increase its market share. His executive committee faces the task of choosing between the two campaigns that have been recommended to him. The committee has decided to test each proposal in two test areas where the initial market shares of the competing companies and the initial transition matrices are equal. Additionally, the companies' market shares are very close to their national average, which is as follows: DMC brand, 28 percent, competitor 1 (Victoria Corp.) 39 percent, and competitor 2 (Johnson Local Electronics Manufacturing), 33 percent. In the two test areas, the holdings are: DMC brand 30 percent, VC brand 40 percent and JLEM brand 30 percent. The matrix of initial transition probabilities for both areas is:

a) Before the application of the programs and according to the data from the initial matrix, are long-term market shares close to the national average?

b) Assuming that the advertising campaigns are equal in terms of costs, which of them gives the higher market share in the long term?

c) For each case, generate the corresponding transition diagram.

Al terminar los dos distintos programas de publicidad en las dos reas de prueba, las probabilidades de transicin que se determinaron fueron las siguientes