Solve the below problem:
Q: A retail store has an annual demand for 30,000 units of one of its products ordered from a wholesaler at a unit cost of $25. The cost of ordering has been estimated to be $10 per order. The company is fortunate in that if the item is not on hand when demanded the customer will wait until the next shipment. Administrative costs of backordering average $6 per unit per week. In addition to this, the retailer reduces the price of the product by $1 per unit for every week that delivery is delayed in order to keep the customer waiting for the order. Storage costs amount to $0.05 per unit per day. Assume a year has exactly 52 weeks or 364 days.
Find:
the optimal order quantity
the optimal backorder quantity
the maximum number of units that will be in stock the
length of the inventory cycle t
he fraction of time a customer has to wait to have his order filled.