Optimization problem of drilling gas fields by one enterprise

A continuous, aggregated dynamic model for the development of gas fields is considered. The drilling of deposits is carried out sequentially by one enterprise. We formulate the problem of maximizing the cumulative accumulated production over a fixed time period with a constraint on capital investment. Simplifying assumptions are made, and the extended problem is solved using the Pontryagin maximum principle. The search for the maximum solution to the original problem is carried out among the solutions to the extended problem. Generalizing conclusions are drawn.