Question

Phillip, the proprietor of a vineyard, estimates that the first 10000 bottles of wine produced this season will fetch a profit of $5/bottle. But if more than 10000 bottles are produced, then the profit per bottle for the entire lot will drop by $0.0002 for each additional bottle sold. Assuming that at least 10000 bottles of wine are produced and sold, what is the maximum profit

Answer 1

$61,250

Step-by-step explanation:

P= (10,000+x)(5-.0002x)= 50,000 +3x -.0002x^2

dP/dx= 3- .0004x

Set equal to zero to find maximum

3-.0004x=0

x= 7,500 so max profit is 61,250