An Auto Company Must Meet (On Time) the Following Demands

An auto company must meet (on time) the following demands for cars: 5000 in quarter 1; 3000 in quarter 2; 6000 in quarter 3; 2000 in quarter 4. At the beginning of quarter 1, there are 500 autos in stock. The company has the capacity to produce at most 3600 cars per quarter. At the beginning of each quarter, the company can change production capacity. It costs $125 to increase quarterly production capacity by one unit. 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 $2400. A holding cost of $200 per car is assessed against each quarter's ending inventory. It is required that at the end of quarter 4, plant capacity must be at least 5000 cars. Determine how to minimize the total cost incurred during the next four quarters.