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The World Health Organization $($WHO$)$ is committed to improving health care in the underdeveloped countries of the world. It currently has five medical teams available to allocate among three such countries to improve their medical care, health education, and training programs. The teams must be kept intact, so the number allocated to each country must be an integer. The measure of performance being used is additional person$-$years of life. For a particular country, this measure equals the increased life expectancy in years times the country$$s population. The following table gives the estimated additional person$-$years of life $($in multiples of $1,000)$ for each country for each possible allocation of medical teams. The WHO would like to know which allocation maximizes the measure of performance.

Number of Teams: $0,1,2,3,4,5$

Country $1$: $0,45,70,90,105,120$

Country $2$: $0,20,45,75,110,150$

Country $3$: $0,50,70,80,100,130$

Formulate and solve this problem using dynamic programming. Show your tables for each step.