The purchasing manager for the Pacific Steel Company must determine a policy for

ordering coal to operate $12$ converters. Each converter requires exactly $5$ tonnes of

coal per day to operate, and the firm operates $360$ days per year. The purchasing

manager has determined that the ordering cost is $$80$ per order, and the cost of

holding coal is $20\%$ of the average dollar value of inventory held. The purchasing

manager had negotiated a contract to obtain the coal for $$12$ per tonne for the

coming year.

What is the optimal quantity of coal to receive in each order $($in tonnes$)?$