Suppose a society consists of three cities (A, B , C. ) with populations of 99,0

Question

Suppose a society consists of three cities (A, B , C. ) with populations of 99,000 , 51,000 , 6,000 people respectively. Suppose that the society has 15 doctors total.

a. What cities will have how many doctors?

b. If the number of doctors doubles to 30. How many will live in each city?

My professor didn't answer it when I asked if I had it correct... but his advice : Calculate the number of doctors per capita in each city for the answer you think is correct. If you cannot move doctors from one city to another in a way that allows that doctor to have more patients in the new city than in the old one, then they are in equilibrium.

Explanation / Answer

City A population = 99000

City B population = 51000

City C population = 6000

Total number of doctors = 15

a)

With 15 doctors for a total of 99,000 + 51,000 + 6,000 i.e 156,000, there will be 1 doctor per 10,400 people.

But city C will need 1 despite of low population,

So city A: 9 doctors, city B: 5 doctors, city C: 1 doctor

b)

If the number of doctors is doubled, there will be 1 doctor per 5200 people,

So ciy C: 2 doctors, city B: 10 doctors and remaining 18 doctors for city A

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