The owner of a vineyard estimates that when 10,000 bottles are produced the profit is $5 / bottle. If more than 10,000 bottles are produced the profit/ bottle decreases by .0002 for each additional bottle. If X represents the number of bottles over 10,000 produced what is the function that gives the profit in terms of X?
What is the total profit when 16,000 bottles are produced?

First line: Profit is given by :

Profit = 5x (for x \leq 10000)

If there is more, say x = 10001, then you have P = 4.9998x.
If you have x = 10002, then P = 4.9996x.
etc.

When 16000 bottles are produced, how many times has the profit per bottle decreased? Then, take that amount, multiply by the number of bottles.

What do you get? :)