Phillip, the proprietor of a vineyard, estimates that the first 9600 bottles of wine produced this season will fetch a profit of $5 per bottle. However, the profit from each bottle beyond 9600 drops by $0.0002 for each additional bottle sold. Assuming at least 9600 bottles of wine are produced and sold, what is the maximum profit? (Round your answer correct to the nearest cent.)

$ ?

What would be the profit/bottle in this case? (Round the number of bottles down to the nearest whole bottle. Round your answer correct to the nearest cent.)

$ ?

To find the maximum profit, we need to calculate the profit for each bottle beyond the first 9600 and see when it starts to decrease.

First, let's calculate the profit for the first 9600 bottles:
Profit per bottle = $5
Number of bottles = 9600
Profit for first 9600 bottles = $5 x 9600 = $48,000

Now, let's calculate the profit per bottle for each additional bottle sold and when it starts to decrease:
Profit drop per bottle = $0.0002
Number of bottles beyond 9600 = (total number of bottles - 9600)

The profit per bottle beyond 9600 can be calculated using the formula:
Profit per bottle = $5 - (Profit drop per bottle × Number of bottles beyond 9600)

Now, let's find when the profit per bottle drops to zero:
$5 - ($0.0002 × Number of bottles beyond 9600) = 0

Rearranging the equation, we have:
Number of bottles beyond 9600 = $5 / $0.0002 = 25000

So, the profit per bottle starts to drop after selling 25000 bottles.

Now, let's calculate the maximum profit by summing up the profits for the first 9600 bottles and the remaining bottles until the profit starts to decrease:
Maximum profit = Profit for first 9600 bottles + (Profit per bottle × Number of bottles beyond 9600)

Maximum profit = $48,000 + ($5 × (total number of bottles - 9600)), where the total number of bottles is rounded down to the nearest whole number.

To find the profit per bottle in this case, we can calculate the profit for the total number of bottles and divide it by the number of bottles.

Considering this, we can now calculate the maximum profit and profit per bottle.