In fish management it is important to know the relationship between the abundance of the spawners (also called the parent stock) and the abundance of the recruits-that is, those hatchlings surviving to maturity.† According to the Ricker model, the number of recruits R as a function of the number of spawners P has the following form for some positive constants A and B. R = APe−BP This model describes well a phenomenon observed in some fisheries: A large spawning group can actually lead to a small group of recruits.† In a study of the sockeye salmon, it was determined that A = 4 and B = 0.7. Here we measure P and R in thousands of salmon. If the number of recruits R is greater than the number of spawners P, then the difference R − P of the recruits can be removed by fishing, and next season there will once again be P spawners surviving to renew the cycle. What value of P gives the maximum value of R − P, the number of fish available for removal by fishing? (Round your answer to two decimal places.) P = thousand salmon
In fish management it is important to know the relationship between the abundance of the spawners (also called the parent stock) and the abundance of the recruits-that is, those hatchlings surviving to maturity.† According to the Ricker model, the number of recruits R as a function of the number of spawners P has the following form for some positive constants A and B.
This model describes well a phenomenon observed in some fisheries: A large spawning group can actually lead to a small group of recruits.† In a study of the sockeye salmon, it was determined that A = 4 and B = 0.7. Here we measure P and R in thousands of salmon.
If the number of recruits R is greater than the number of spawners P, then the difference R − P of the recruits can be removed by fishing, and next season there will once again be P spawners surviving to renew the cycle. What value of P gives the maximum value of R − P, the number of fish available for removal by fishing? (Round your answer to two decimal places.)
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