Question

Hester’s Hatchery raises fish. At the end of the current season she has 3,000 fish in the hatchery. She can harvest any number of fish that she wishes, selling them to restaurants for $10 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 $10 each next year as well. Hester relies entirely on income from current fish sales to support herself Suppose Hester's goal is to have an equal amount of income in each year.

Under this strategy, Hester should harvest _____ fish in the current year. Her current year's income will be $_____ . Under this strategy, Hester should leave_____ fish in the hatchery this year, which will produce____ fish next year. Her second year's income will be $____ . Her total income in two years will be $____ .

Answer 1

Let the number of fish sold = X

Number of fish left = 3000-X

Total number of fish available for sell = 2*(3000-X)

X=2(3000-X) = 2*3000-3X=3X=2*3000=2(3000/3)=2*1000=2000

Under this strategy, Hester should harvest 2000 fish in the current year. Her current year's income will be $2000*10=$20000. Under this strategy, Hester should leave 1000 fish in the hatchery this year, which will produce 1000 fish next year. Her second year's income will be 2000*10=$20000 . Her total income in two years will be $40000