Gambit buys and sells children's playground equipment. The company buys swings from a manufacturer for $100 for each swing. Gambit sells the swings for $300. The manufacturer delivers swings to Gambit and bears the delivery costs of $200 per shipment. Each time of ordering, Gambit needs to spend $150 per order in paperwork and inspection. On average, there is a lead time of 12 days for each order to arrive from the manufacturer to Gambit's warehouse. Inventory carrying/holding cost for Gambit is 5%. Average yearly demand for the swings is 150,000 units. Answer the following questions, assuming there is no uncertainty at all about the demand. 

(a) How many swings should Gambit order each time? 

(b) Now the lead time went up from 12 to 15 days, how should Gambit change the order quantity and the reorder point of swings: increase, decrease, or stay the same, and why? 

(c) There are several assumptions in the problem description enabling you to do the calculation in 

(a). Please list the key assumptions. Which assumptions do you think are the most unrealistic? 

Suppose Gambit uses the order quantity that you calculated in 

(a), what is the impact on its inventory and logistics management if these unrealistic assumptions are relaxed?