The estimated demand for a product at the Little Jimmy Store is 4,000 units per year. The estimated ordering cost is \(\$ 30\) per order and the estimated carrying cost is \(\$ 5\) per unit per year. The stockout cost is estimated to equal \(\$ 10\) per unit. The manager of the store has used the estimated data and the EOQ model with stockouts to determine the optimal order quantity

{Required:}

(1) What is the optimal order quantity and how much is the expected total inventory cost of the optimal inventory policy?

(2) Calculate the value of the perfect information for the true carrying cost of \(\$ 4\) instead of \(\$ 5\) per unit [assume: (1) all estimates except the carrying cost are correct, and (2) without the knowledge of the true carrying cost, the manager's original solution will be implemented for a full year].