Q$.$ An automobile company assembles cars in a plant and purchases batteries from a vendor in China. The average cost of each battery is $$45.$ The automobile company takes ownership of the batteries when they arrive at the plant. It takes exactly $12$ hours to make a car in the plant and the plant assembles $200$ cars per $8-$hour shift. Each car uses one battery. The company holds, on average, $8000$ batteries in raw material inventory at the plant as a buffer.

i$.$ What is the total number of batteries in the plant?

ii$.$ How many days of supply is held in raw material inventory, on an average?