Question 3: Tobias Nagy is the merchandise planner for Cellular Junction, a chain of retail stores that sell mobile phones paired with contracts from all of the major cellular providers. The chain's most popular offering is a low-cost smartphone manufactured by a Chinese company known as GSB. The phones are so cheap, however, that the name "GSB" is not even printed on the phone itself. The phones are simply sold as generic unit bundled with a two-year contract for cellular phone and data service. As a result, cost is of significant concern for Cellular Junction as well as for GSB. To reduce the cost of the item, GSB manufactures its phones on dedicated assembly lines at its facility in Tianjin, China. The phones are shipped to GSB via ocean freight, and it takes shipments approximately 20 weeks to arrive at Cellular Junction's distribution center in Columbia, South Car- olina, once it places an order to GSB. This long order cycle time prevents Cellular Junction from placing any replenishment orders for a particular model of phone because the technology changes so quickly that new models are released approximately every six months. Cellular Junction sells the phones for $69 each with a two-year contract. The total value of the contract, after expenses, is estimated to be $500. It purchases the phones from GSB for $99 each, and the ocean shipping cost is estimated to be an additional $5 per unit. Any phones left over when a new model is released are liquidated to a secondary retailer for $49 each (with no additional revenue from a service contract). Cellular Junction estimates that its demand for the current model of phones across all of its stores follows a normal distribution with a mean of 5,000 units and a standard deviation of 1,200 units. a. Determine the optimal quantity of each new model of mobile phone that Cellular Junction should order to maximize its expected profit.