math
posted by Julie 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.)
$ ?

profit/bottle is 5.00  0.0002(x9600) for x bottles, x > 9600
total profit is thus
p(x) = 5*9600 + (x9600)(5.00  0.0002(x9600))
= .0002x^2 + 8.84x  18432
This is a parabola opening downward, with vertex at x = 22100
p(22100) = 79250