Pullman Tire Company would like to plan production for the next three months. The firm can satisfy demand by using inventory, regular production (at $40 per tire), overtime (at $50 per tire), or subcontracting (at $70 per tire). Any tires held over for one month incur a $2 per tire inventory carrying cost. Pullman Tire has sufficient regular production capacity to produce up to 700 tires each month, and it can produce up to 50 more tires each month using overtime. The subcontracting availability from an alternative supplier is 150 in January and February and 130 in March. Customers will demand 650 tires in January, 1,000 in February, and 890 in March (all demand must be satisfied on time; i.e., no backorders are allowed). The firm begins with 100 tires and wants to have no tires left in inventory at the end of March. Formulate a linear program for this problem, and determine the cheapest tire production plan after solving the problem in Excel.