Phillip, the proprietor of a vineyard, estimates that the first 9500 bottles of wine produced this season will fetch a profit of $3 per bottle.

Question

Assuming at least 9500 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.)

Answer 1

Extending Raymond’s answer to include the additional problem definition: The first 9500 bottles each generate $3.00 in profit, but each subsequent bottle generates $0.0003 less. Which bottle is the last one with positive profit, that is, confers $.0003 profit?

The 19500th bottle.

Any bottles beyond that generate negative profit, I suppose. So the max total profit is for 10000+9500 = 19500 bottles.

At that point, the total profit of the 10000 bottles is $1.50 * 10000, so the total profit is

$1.50 x 10000 + $3 x 9500 = $15000 + $28500 = $43500.

Divide that by total bottles 19500 to get average profit per bottle to get

$43500 / 19500 = $2.23

Answer 2

9500 x $3 = $28,500 minimum profit

maximum profit is infinity times $3 = infinity dollars

profit per bottle is a constant $3 per bottle whether at a max or min profit or anywhere in between