During the next four quarters, an automobile company must meet (on time) the following demands for ...

During the next four quarters, an automobile company must meet (on time) the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3; 1000 in quarter 4. At the beginning of quarter 1, there are 300 autos in stock. The company has the capacity to produce at most 3000 cars per quarter. At the beginning of each quarter, the company can change production capacity. It costs 100 to increase quarterly production capacity by 1 unit. For example, it would cost 20,000 to increase capacity from 3000 to 3200. It also costs 60 per quarter to maintain each unit of production capacity (even if it is unused during the current quarter). The variable cost of producing a car is 2200. A holding cost of 160 per car is assessed against each quarters ending inventory. It is required that at the end of quarter 4, plant capacity must be at least 4000 cars. Determine how to minimize the total cost incurred during the next 4 quarters.