The manager of a fishery determines that t weeks after 3000 fish of a particular
ID: 3348282 • Letter: T
Question
The manager of a fishery determines that t weeks after 3000 fish of a particular species are hatched, the average weight of an individual fish will be w(t)= 0.8te^(-0.05t) lbs, for 0< or = t < or = 20. Moreover, the proportion of fish that will still be alive after t weeks is estimated to be p(t) = 10 / 10 + t.
a) Express the expected yield E(t) (total weight pf the fish that remain alive) in terms of w(t) and p(t).
b) For what value of t is the expected yield largest? What is the maximum expected yield?
Explanation / Answer
a) E(t) = p(t)* w(t)
b) dE/dt = 0 , d( 0.8te^(-0.05t)* 10/(10+t)) = 0
-(2*x^2+20*x-400)*%e^-(x/20)/(5*x^2+100*x+500) = 0
t= 20 weeks
Max yield = 1.962 lbs
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