Tobacco use in young people has a considerably negative impact on public health, which has been linked to four out of six leading causes of death internationally. For this reason, in January 2021, the Government of Mexico City, the Ministry of Finance and Public Credit (SHCP) and the Ministry of Health (SSA) have determined to apply a tax of 15% to the price of cigarette packs. Andrs Joaqun is a smoking student who is not aware of the context described above. He studies engineering and receives a monthly scholarship of $ 9,500 pesos. Of the previous amount, he dedicates 10.52% to the purchase of cigars (x) and beers (y), and his preferences for both goods can be represented as: U (x, y) = x ^ 0.3 y ^ 0.7 Using the lagrange method, estimate the demand functions (x ^ m and y ^ m) for Andrs' cigarettes and beers. (20 points) What is the optimal basket of cigars and beers, which Andrs will demand given the monthly budget that he dedicates to both goods. This knowing that the price of packs of cigarettes is $ 45 pesos and that of beers is $ 14. (10 points) With the available data, graphically describe what will happen to the demand for cigarettes and beers when Andrs finds out that his prices have risen.