The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are D = 800 units, S = $25/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

Quantity	1 to 49	50 to 249	250 and up
Price	$5.00 per unit	$4.50 per unit	$4.10 per unit

Q2

An electric toy car manufacturer Baranka makes its own wind-up motors, which are then put into its cars. While the toy manufacturing process is continuous, the motors are intermittent flow. Baranka has an annual demand of 50,000 cars. It costs $90 to set up production process and 20 cents to hold one unit per year. Baranka's daily manufacturing capability is 1,000 units, and ships 200 units to the customers daily.

(1) What is the optimal manufacturing batch?

(2) What is Baranka's average inventory?