In this paper, we are interested by a stochastic model of production of an exhaustible resource, such as oil. It is known that such reserves are depleted resources, but there is a possibility of exploration and discovery of new reserves which ensure the accumulating or the upkeep of this reserves' level. We modelled the new discoveries by a jump process with intensity given by the exploration effort. We employed a weak formulation of the standard martingale optimality principle to solve a linear quadratic stochastic control problem for mean field stochastic differential equation with jumps in both cases: finite and infinite horizon.