The manager of a fishery determines that t weeks after 3,000 fish of a particular species are hatched, the average weight of an individual fish will be w(t) = 0.8te^−0.05t pounds, for 0 ≤ t ≤ 20. Moreover, the proportion of the fish that will still be alive after t weeks is estimated to be

a. The expected yield E(t) from harvesting after t weeks is the total weight of the fish that are still alive. Express E(t) in terms of w(t) and p(t).

b. For what value of t is the expected yield E(t) the largest? What is the maximum expected yield?

c. Sketch the yield curve y = E(t) for 0 ≤ t ≤ 20.

Transcribed Image Text:

p(t) = 10 10 + t