  We consider an additional food provided prey-predator model exhibiting
Holling type IV functional response with combined continuous white noise and
discontinuous L\'evy noise. We prove the existence and uniqueness of global
positive solutions for the considered model. By considering the quality and
quantity of additional food as control parameters, we formulate a time-optimal
control problem. We obtain the condition for the existence of an optimal
control. Furthermore, making use of the arrow condition of the sufficient
stochastic maximum principle, we characterize the optimal quality of additional
food and optimal quantity of additional food. Numerical results are given to
illustrate the theoretical findings with applications in biological
conservation and pest management.
