A manufacturer of Bluetooth headphones examines the historical demand of its product and learns that the average monthly demand is about $3,450$ headphones but varies between $2,450$ and $4,030$ headphones. Each pair of the headphones has a retail price of $$70.$ The monthly fixed production cost ranges from $$5,100$ to $$10,000,$ with an average of $$9,600.$ The average variable cost of producing a pair of headphones is $$43,$ but because the manufacturing process is not fully automated, the variable cost may vary between $$38$ and $$43$ per pair. Develop a risk analysis model to answer the following questions.

What is the monthly profit from the Bluetooth headphones for the most likely, pessimistic, and optimistic scenarios?

The company notices that during the holiday season in December, the demand tends to be higher than in other months. Historically, the demand in December is about $3,938$ pairs on average, but also ranges from $2,635$ to $4,687$ pairs. What is the December profit for the most likely, pessimistic, and optimistic scenarios?