Mathematical modeling of a case of sustainable exploitation of a biological species

We pose the problem of the introduction of a biological species in an ecosystem in order to a future exploitation. For the first vivarium stage, we have obtained a simple method to determine the parameters of the logistic equation, which determines the growth of the species, from two experimental measures of the number of individuals. For the second phase of exploitation, we have obtained an expression for the maximum exploitation rate (number of individuals caught per unit time) for it to be sustainable, that is, the population does not become extinct. In the event that the exploitation rate is higher than the maximum that ensures sustainability, we provide an expression for the time of extinction. It has also obtained an expression for the minimum time that must have the vivarium stage to maximize sustainable harvest rate.