Periodic preventive maintenance is carried out on aircraft engines, where an important component must be replaced. The number of aircraft scheduled for such maintenance over the next 6 months is estimated at 200,180, 300,198,230, and 290, respectively. All maintenance work is done in the month that parts are available, where a used component may be replaced with a new or an overhauled component. The overhauling of used components may be done in a local repair facility, where they will be ready for use at the beginning of next month, or they may be sent to a central repair shop where a delay of 2 months (as such maintenance can occur in the third month) is expected. The repair cost in the local shop is $120 per component. At the central facility, the cost is only $35 per component. An overhauled component used in a later month will incur an additional storage cost of $1.50 per unit per month. New components may be purchased at $200 each in month 1, with a 5% price increase every 2 months. A new component is available immediately (no delay). Formulate a model to the problem and solve to determine the optimal schedule for satisfying the demand for the component over the next 6 months. Also consider that the planning occurs within the first month. So all parts are ordered in the first month to satisfy maintenance requirements.