Mark a fish farmer wants to know when he should sell his farm to maximise profits. He has lake that contains 12000 fish. They grow at the rate of 1.6% each month and he harvest 359 at the end of each month and sells them for $150 each.
a) How long until there are no fish
b) A nearby fish farmer is keen to buy mark's fish farm and each month after harvest, he offers Mark $16 per fish for remaining stock. After how many months would be the best time to sell in order to maximise his profits?