The government has assigned you to lead their aid program. They are willing to spend 1%...

 

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The government has assigned you to lead their aid program. They are willing to spend 1% of the national gross product of b SEK. They are considering to give aid to a set of countries N = {1,....N). The aim of the aid program is to increase the Human Development Index (HDI) in the countries which is calculated by measuring the three factors education per capita, life expectancy and gross national product per capita (GDP). We may therefore consider the HDI index as a measure of development per capita in a country. For all countries jeN let a, denote the current value of the HDI index, c, the increase of HDI per SEK given as aid to the country and p, the population size. There are only a limited number of aid programs in each of the countries. This puts a limit on the maximal aid that a country can receive, let d, SEK denote the maximal aid country j can receive. (a) Write a linear program for distributing aid that maximizes the HDI in the region formed by all the countries considered. (b) You are given new directives from the government, they think that the aid should be focused on a maximal number of M countries. Introduce integer variables in your model (i.e. write an Linear Integer Programming model) in order to accommodate this demand. (c) There has recently been some discussion concerning aid to countries with high HDI. The government wants you to write a new model that maximizes the minimal HDI among the countries. Extend your model in a) to an LP model that accommodates this demand The government has assigned you to lead their aid program. They are willing to spend 1% of the national gross product of b SEK. They are considering to give aid to a set of countries N = {1,....N). The aim of the aid program is to increase the Human Development Index (HDI) in the countries which is calculated by measuring the three factors education per capita, life expectancy and gross national product per capita (GDP). We may therefore consider the HDI index as a measure of development per capita in a country. For all countries jeN let a, denote the current value of the HDI index, c, the increase of HDI per SEK given as aid to the country and p, the population size. There are only a limited number of aid programs in each of the countries. This puts a limit on the maximal aid that a country can receive, let d, SEK denote the maximal aid country j can receive. (a) Write a linear program for distributing aid that maximizes the HDI in the region formed by all the countries considered. (b) You are given new directives from the government, they think that the aid should be focused on a maximal number of M countries. Introduce integer variables in your model (i.e. write an Linear Integer Programming model) in order to accommodate this demand. (c) There has recently been some discussion concerning aid to countries with high HDI. The government wants you to write a new model that maximizes the minimal HDI among the countries. Extend your model in a) to an LP model that accommodates this demand

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