A contractor undertakes to supply diesel engines to a truck manufacturer at the rate of 30 per day. He finds that the cost of holding a completed engine in stock is $ 18 per month. Production of engines is in batches and each time a new batch is started, there are set-up costs of $ 10,000. How frequently should the batches be started and what will be the minimum average inventory cost and production time if production rate is 40 engines/day. Assume 300 working days in a year.