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During the next four quarters Dorian Auto must meet (on time) the following demandsfor cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3; 1000 in quarter 4. At thebeginning of quarter 1, there are 300 cars in stock. The company has the capacity toproduce at the most 3000 cars per quarter. At the beginning of each quarter, the companycan increase (but not decrease) its production capacity. It costs $100 to increaseproduction capacity by one unit. For example, it would cost $10,000 to increaseproduction capacity from 3000 cars per quarter to 3100 cars per quarter. It also costs $50per quarter to maintain each unit of production capacity (whether it is used or not). Thevariable cost of producing a car is $2000. A holding cost of $150 per car is assessed foreach quarter?s ending inventory. It is required that at the end of quarter 4, plant capacitymust be at least 4000 cars.
(1) Determine how to minimise the total cost incurred during the next four quarters.There is a concern that due to rising material and labor costs the variable cost in thefourth quarter may increase by 10%.
(2) Should you change your production plan if you believe this increase will occur?
(3) What would you do if you believed that there would be a 20% increase in variablecosts in the fourth quarter?
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