Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $4/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold.
Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?

A) The maximum profit is $30,000.00, the price/bottle is $3.70/bottle
B) The maximum profit is $40,000.00, the price/bottle is $4.00/bottle
C) The maximum profit is $35,000.00, the price/bottle is $3.90/bottle
D) The maximum profit is $25,000.00, the price/bottle is $3.60/bottle
E) The maximum profit is $20,000.00,the price/bottle is $4.00/bottle

Question

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $4/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold. ​
Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?
​
A) The maximum profit is $30,000.00, the price/bottle is $3.70/bottle
B) The maximum profit is $40,000.00, the price/bottle is $4.00/bottle
C) The maximum profit is $35,000.00, the price/bottle is $3.90/bottle
D) The maximum profit is $25,000.00, the price/bottle is $3.60/bottle
E) The maximum profit is $20,000.00,the price/bottle is $4.00/bottle

Quizplus · Accepted Answer

The maximum profit from the first 10,000 bottles is $40,000 ($4/bottle). Beyond 10,000 bottles, the profit decreases, so it cannot exceed this initial amount. Therefore, the maximum profit is when only the first 10,000 bottles are sold at $4/bottle.

Phillip, the Proprietor of a Vineyard, Estimates That the First