Posted by shannon on .
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.)
well it'll be about 25 bottles sold before the profit changes; 5.00 will become approximately 4.99 after 25 bottles sold (0.005 rounds off to 0.01). after the first 25, the profit won't change to 4.98 until 50 bottles are sold. (0.015 will round off to 0.02) the 50 bottles per cycle will continue through out the process;
25 bottles sold = $125 profit ($5*25)
75 bottles sold = $125 + $249.5 ($4.99*50)
125 bottles sold = $374.5 + ($4.98*50)
continue this process and you will find the answer once you reach 9600 bottles.
For the second part; take the answer from the first question and divide it by 9600.