Question 3. Consider a warehouse and a retailer operating in a deterministic demand environment where no shortages are allowed at the retailer. The warehouse orders the same quantity as the retailer. The warehouse purchases each unit for $5 and sells to the retailer at $8. The retail price is $14. The fixed replenishment costs of the warehouse and the retailer are $500 and $100, respectively. The retailer also incur a cost for carrying one unit of inventory for unit time, which is $2.3/ item/year. The end customer demand for this item is 20,000 units per unit time. a) What is the optimal order quantity of the retailer? b) What is the total average cost of the retailer? c) What is the profit of the warehouse? d) How can the warehouse encourage the retailer to increase his order size by a factor of K ? What is the value of K ? What is the new order quantity of the retailer? e) What would be the total average cost of the retailer if he orders the quantity found in part d? f) What would be the new profit of warehouse? Is the warehouse better off