The new Toyota production plant starting up in Guanajuato, in central Mexico would be manufacturing a radical new Corolla Compact that will go on sale in 2020. In order to make appropriate capacity and design decisions for the plant, the operations unit at Toyota has to compute the optimal inventory and productions levels needed to meet global demand in a cost effective fashion. It has been forecasted that the annual demand for the new Corolla is going to be 150,000 and the plant works 350 days/yr. The daily production capacity is 580 Corollas. The setup cost to start a production run is $10,000 and the annual inventory carrying cost is $1000 per Corolla per year.

What should be the optimum number of Corollas to be produced in a production run?
What is the maximum inventory achieved during a production run?
What is the average inventory of Corollas throughout the year?

What is the total annual cost of setting up production runs and holding inventory?