Hester’s Hatchery raises fish. At the end of the current season she has 6,000 fish in the hatchery. She can harvest any number of fish that she wishes, selling them to restaurants for $5 a piece. Because big fish make little fish, for every fish that she leaves in the hatchery this year, she will have two fish at the end of next year. The price of fish is expected to be $5 each next year as well. Hester relies entirely on income from current fish sales to support herself.
a. How many fish should Hester harvest if she wants to maximize the growth of her stock of fish from this season to next season?
Thank you for the opportunity to help you with your question!
First of all, raising fish costs money. Hester basically needs the least money that can cover raising the left fish. According to the logic in the context, 1 fish produce 2 fish, which means a cost to raise a fish is half price of $5, equaling to $2.5. So the interest of selling fish should cover the next year cost of raising fish. Grant selling number is x, than 5x = (6000-x)*2.5. So x = 2000. If Hester wants to maximize the growth of her stock of fish from this season to next season, she needs to sell 3000 fish.
Please let me know if you need any clarification. I'm always happy to answer your questions.