Question

Hester’s Hatchery raises fish. At the end of the current season she has 2,100 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.

e. Suppose Hester's goal is to have an equal amount of income in each year.

Instructions: Enter your responses as integer values.

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

Consider the given problem here “Hester’s Hatchery” raises fish, currently she has 2,100 fishes in the hatchery and the price of fish is “$5” per piece and will remain same in the next season.

Now, number of fish will grow by the big fish. So, if she has 1 big fish then the number of fish will be 2 at the end of the season. Now, her objective is to earn equally in both the years, => she have to sell equal numbers of fishes to the restaurant in each year.

Let’s assume that “X” be the number of fishes she sell in the restaurant in the current year, => the numbers fishes left for the 2^nd year is (2,100 – X). So, total number of fishes available for sell is “2*(2,100 – X)”.

Now, because she want the same level of income, => she should supply same amount of fishes to the restaurant.

=> X = 2*(2,100 – X ) = 2*2,100 – 2*X, => 3*X = 2*2,100 = 2*(2,100 / 3) = 2*700 = 1,400.

So, currently she should supply “1,400” fishes => her current income will be 5*1,400 = $7,000.

=> Now, she will harvest “1,400” fishes and will leave “700” fishes that will be “2*700 = 1,400, => the level of income in the 2^nd year is 5*1,400 = $7,000.

=> Under this strategy, Hester should harvest “1,400” fishes in the current year.

=> Her current year's income will be $7,000.
=> Under this strategy, Hester should leave “700” fishes in the hatchery this year, which will produce “700” fishes next year.
=> Her second year's income will be $7,000.  
=> Her total income in two years will be $14,000.