Real-World Applicationshard
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A fish population grows according to the logistic equation with harvesting: fracdPdt=0.4Pleft(1fracP10000right)H\\frac{dP}{dt} = 0.4 P \\left( 1 - \\frac{P}{10000} \\right) - H, where the harvest rate is H=qEPH = q E P with catchability q=0.0001q = 0.0001 and fishing effort EE. What effort EE maximizes the steady-state harvest rate (Maximum Sustainable Yield)?