Question: Federal or state agencies control hunting and fishing by setting a quota on how many animals can be harvested each season. Determining the appropriate quota means achieving a balance between environmental concerns and the interests of hunters and fishers. For example, when a June 8, 2007 decision by the Delaware Superior Court invalidated a two-year moratorium on catching horseshoe crabs, the Delaware Department of Natural Resources and Environmental Control imposed instead an annual quota of 100,000 on male horseshoe crabs. Environmentalists argued this would exacerbate a decrease in the protected Red Knot bird population that depends on the crab for food. For a population P that satisfies the logistic model with harvesting,
(dP/dt) =kP(1 - (P/L)) - H,
show that the quota, H, must satisfy H ≤ kL/4, or else the population P may die out. (In fact, H should be kept much less than kL/4 to be safe.)