1. (5 points) A rail company wishes to optimize the beverages it will carry on board its trains to be sold to its passengers as part of its catering service. The company operates three routes linking the cities of Seville (Sev), Madrid (Mad) and Barcelona (Bar). The following information is given in the table: . to maintain service quality levels, there is a minimum amount of beverages that should be carried on board for any of the trains, . the company has estimated the maximum amount (demand) that passengers might want to buy, . the price depends on the city the train comes from, due to local taxes, . the unit cost depends on both the city of departure and the destination. Departure-destination Sev-Mad Sev-Bar Mad-Bar Mad-Sev Bar-Sev Bar-Mad Minimum requirement 60 108 150 74 156 96 Estimated demand 108 141 184 96 192 240 Unit price 2.5 2.5 2.75 2.75 3 3 Unit cost 1.78 1.60 1.19 1.91 1.80 2.01 Price and cost are given in euros per liter, demand is given in liters, and we assume the beverages can be sold in any fractions of liters desired by the passengers. Your goal is to help the company decide the amount of beverages to carry in each route, while satisfying the following conditions: . You have a maximum total budget equal to 1600 euros for all the routes. . Due to the warm weather in Seville, the beverages to be carried in the trains that depart from this city must be stored using a special cooling system, with a capacity of 215 (liters) for all routes departing from Seville. . The company wishes to transport the same amount of beverages in both directions between any given two cities. Thus, you are going to send the same amount from Seville to Madrid than from Madrid to Seville. This is true for all pairs of cities. . The amounts of beverages that you carry should be larger than the minimum requirements for the route. . The amount of beverages carried in one route should not exceed the maximum of the estimated demands for both directions in that route