Question

Phillip, the proprietor of a vineyard, estimates that the first 10900 bottles of wine produced this season will fetch a profit of $6 per bottle. However, the profit from each bottle beyond 10900 drops by $0.0001 for each additional bottle sold. Assuming at least 10900 bottles of wine are produced and sold, what is the maximum profit

Answer 1

See below

Step-by-step explanation:

With regards to the above information, we can write out the equation to be;

P = (10,900 + y)($6 - 0.0001y)

= 65,400 - 1.09y + 6y - 0.0001y^2

= 65,400 + 4.9y - 0.0001y^2

dp/dx = 4.9 - 0.002y

Set equal to zero to find maximum

4.9 - 0.002y = 0

y = 8,000

So, maximum profit is $