Operations Management: Homework Assignment $4$

Due on $11$:$59$pm$,$ April ${29}^{th},2024$

Q$3.$ Dallas Mavericks' owner Mark Cuban proved his business intelligence once again with the acquisition of star player Kyrie Irving. To benefit from this blockbuster trade even further, Cuban plans to sell one$-$time$-$only special edition Irving 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?

b$.$Cuban also plans to sell these special edition jerseys in his vacation resort. Knowing thst 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 orpanage. Cuban estimates the demand for the jerseys during in the resort by the following distributions, with P$()$ being the probability distrubution. Number of jerseys $30,60,90,120,150.$ P$($number of jerseys$)\mathrm{.}1,\mathrm{.}25,\mathrm{.}4,\mathrm{.}2,\mathrm{.}05$