Q1. Dallas Mavericks' owner Mark Cuban proved his business intelligence once again with the acquisition of star player Kristaps Porzingis. To benefit from this blockbuster trade even further, Cuban plans to sell one-time-only special edition Porzingis jerseys at a price of $380 each during the first month of the season. The production cost for each of these jerseys would be $100 thanks to their golden details, and any unsold jersey during October will be sold for $80 during November. Knowing the fan base for years, Cuban estimates demand for these special edition jerseys to follow a normal distribution with a mean of 10,000 units and a standard deviation of 2,000.

a)The design process, sourcing, production and shipping of these jerseys take about two months. Hence, Cuban has one opportunity to place a production order and receive these orders on time (before October) for sale. Determine the optimal number of special edition jerseys that Cuban should produce? (5 points)

b)b. Cuban also plans to sell these special edition jerseys in his vacation resort. Knowing that people are wealthier in the resort, he sets a price of $500 for each jersey (although production cost stays the same). This time however, he cannot sell any unsold jerseys outside the resort and will simply donate them to an orphanage. Cuban estimates the demand for the jerseys during in the resort by the following distribution, with P() being the probability distribution.

Number of Jerseys P(Number of Jerseys)

30 0.10

60 0.25

90 0.40

120 0.20

150 0.05

How many special edition jerseys should Cuban produce to sell in his resort? (5 points)