There's a zombie outbreak in a city of 20 million people and the army has been ordered to deal with it. Since you are the general, that means you...

There's a zombie outbreak in a city of 20 million people and the army has been ordered to deal with it. Since you are the general, that means you have to decide what to do. One option is that you could send in all of your troops, but then you would have none to spare if there's another outbreak somewhere else. Instead, you decide to send in a smaller force of just 2,000 soldiers with orders to recruit members of the public to help them fight the zombies. This solution leaves you with plenty of soldiers in case there are any other outbreaks, but no one else thinks it will work. To prove them wrong, you set out to do the calculations. You know that each soldier can hunt down and kill 15 zombies a day. In the evening, each soldier can also recruit one new soldier from the people in the city who will join the army the following day and fight the zombies. However, each night, the zombies will fight back and each one will infect five normal people who then become zombies. You know that there are currently 60,000 zombies in the city.