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 one unit. For example, it would cost $10,000 to increase capacity from 3000 to 3100. It also costs $50 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 $2000. A holding cost of $150 per car is assessed against each quarter’s ending inventory.

At the end of quarter 4, plant capacity must be at least 4000 cars.

a. Determine how to minimize the total cost incurred during the next 4 quarters.

b. Use SolverTable to determine how much the total cost increases as the required capacity at the end of quarter 4 increases (from its current value of 4000).