24 During the next four quarters, Dorian Auto must meet

(on time) the following demands for cars: quarter 1—4,000;

quarter 2—2,000; quarter 3—5,000; quarter 4—1,000. At the beginning of quarter 1, there are 300 autos in stock, and the company has the capacity to produce at most 3,000 cars per quarter. At the beginning of each quarter, the company can change production capacity by one car. It costs $100 to increase quarterly production capacity. It costs $50 per quarter to maintain one car of production capacity (even if it is unused during the current quarter). The variable cost of producing a car is $2,000. A holding cost of $150 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 4,000 cars. Formulate an LP to minimize the total cost incurred during the next four quarters.