Question

The proprietor of a vineyard estimates that if 10,000 bottles of wine were sold this season, then the profit would be $7.50/bottle. But if more than 10,000 bottles were produced, then the profit per bottle for the entire lot would drop by $0.00025 for each additional bottle sold. Assuming that at least 10,000 bottles of wine are sold, and let x denote the number of bottles produced and sold in excess of 10,000.

a. Determine the quadratic profit function P x( ) that represents the profit the vineyard can expect from the number of bottles produced and sold in excess of 10,000. (must be completely simplified)

b. Determine the profit from a sale of 16,000 bottles of wine

c. If the vineyard made $60,000 in profit, how many bottles of wine did he sell?

d. Find the number of bottles the vineyard needs to sell in order to maximize their profits .(do not use derivatives)

e. What is the maximum profit? (do not use derivatives)

Answer 1

Manu mum t lo 000 latus 56.25 x(0 00025 56,250 ou)x.ro 62o