To supply their technology, factories consume steam and electricity. These inputs may be generated internally or purchased in the market. To do it internally, some factories inside its power plant use a heat pump, together with a steam boiler and a condensation turbine. For selection of the optimal inputs in real time, the cost region diagram is derived by using mixed integer linear programming. When used, this diagram might maximally enable an expense saving up to 88.8%, depending on the costs of the internal energy inputs. These savings could be even greater if the steam boiler could satisfy the factory energy consumption completely. Generally, the use of these diagrams enables control of complex energy industrial systems without employing powerful computers.