QUESTION 7 The home fitness company Peloton sells two versions of their popular exercise bicycles, the standard Bike and the premium Bike+ (pronounced "bike plus"). Both the Bike and the Bike+ have mounted touchscreens and audio systems to connect the ride with online fitness classes, but the Bike+ has a larger screen and better sound quality. Based on historical sales data, they have estimated that the weekly demand in Los Angeles for their exercise bicycles is equal to 80 - p/50, where p is the price of the bicycle. Peloton charges $1,800 for the Bike and $2,500 for the Bike+. Customers only buy one type of exercise bicycle, meaning the high willingness to pay customers buy the Bike+ and the low willingness to pay customers buy the Bike. Peloton's supply chain partner charges $3,000 per shipment from the base manufacturer to Peloton's Los Angeles distribution center, regardless of the number or type of bicycles in the delivery. Peloton has assessed that the annual cost of storing a bicycle at their LA distribution center is $200 per bicycle due to the necessary upkeep of the machines. It takes 4 weeks for a shipment to be delivered to Peloton's distribution center in LA from the time it is placed with the base manufacturer. Peloton's LA distribution center is operational 52 weeks a year. a. (5 points) What is the weekly demand in LA for each type of bicycle and what is Peloton's resulting annual total sales revenue? b. (5 points) If Peloton places separate orders for each type of bicycle, what is the optimal order size for each? C. (5 points) Peloton realized that since they are ordering all these bicycles from the same supplier, it may be a good idea to combine shipments. Keeping the prices for all products the same, how many of each type should Peloton order every time they make an order? d. (5 points) How much is Peloton saving annually from combining the orders? Peloton has recently considered introducing the Bike* (pronounced "bike star), which would be a single middle-ground product between the Bike and Bike+, with some premium qualities of the latter while retaining some of the affordability of the former. This would be Peloton's only offered product, replacing both Bike and Bike+. e. (5 points) Assuming that the demand equation for the Bike* is the same as before, what is the price that maximizes revenue for this single product and what is their new annual sales revenue? f. (2 points) Using the price from part (e) and assuming the same fixed shipping fee and annual stocking cost as before, how many Bike* units should Peloton order at each shipment? g. (8 points) Assuming that Peloton can only order once every four weeks and that the manufacturing cost of each bicycle is $500, what is the profit maximizing price? Fixed shipping fee and annual stocking cost remain the same. h. (2 points) After reviewing the historical sales data report, Peloton has realized that the analytics firm that calculated the and equation also provided a standard deviation equal to 12.5 records and if Peloton can tolerate a stockout probability of at most 5%, at what number of Bike* should they place their next order if each Bike* is priced at $2000? Recall that the lead time is 4 weeks. (Hint: Z(0.95) = 1.64.) i. (3 points) If Peloton decides to sell all three types of bicycles, the Bike at $1,500, the Bike* at $2,200, and Bike+ at $3,000 [note these numbers have changed versus the prices above], what would be Peloton's annual revenue? QUESTION 7 The home fitness company Peloton sells two versions of their popular exercise bicycles, the standard Bike and the premium Bike+ (pronounced "bike plus"). Both the Bike and the Bike+ have mounted touchscreens and audio systems to connect the ride with online fitness classes, but the Bike+ has a larger screen and better sound quality. Based on historical sales data, they have estimated that the weekly demand in Los Angeles for their exercise bicycles is equal to 80 - p/50, where p is the price of the bicycle. Peloton charges $1,800 for the Bike and $2,500 for the Bike+. Customers only buy one type of exercise bicycle, meaning the high willingness to pay customers buy the Bike+ and the low willingness to pay customers buy the Bike. Peloton's supply chain partner charges $3,000 per shipment from the base manufacturer to Peloton's Los Angeles distribution center, regardless of the number or type of bicycles in the delivery. Peloton has assessed that the annual cost of storing a bicycle at their LA distribution center is $200 per bicycle due to the necessary upkeep of the machines. It takes 4 weeks for a shipment to be delivered to Peloton's distribution center in LA from the time it is placed with the base manufacturer. Peloton's LA distribution center is operational 52 weeks a year. a. (5 points) What is the weekly demand in LA for each type of bicycle and what is Peloton's resulting annual total sales revenue? b. (5 points) If Peloton places separate orders for each type of bicycle, what is the optimal order size for each? C. (5 points) Peloton realized that since they are ordering all these bicycles from the same supplier, it may be a good idea to combine shipments. Keeping the prices for all products the same, how many of each type should Peloton order every time they make an order? d. (5 points) How much is Peloton saving annually from combining the orders? Peloton has recently considered introducing the Bike* (pronounced "bike star), which would be a single middle-ground product between the Bike and Bike+, with some premium qualities of the latter while retaining some of the affordability of the former. This would be Peloton's only offered product, replacing both Bike and Bike+. e. (5 points) Assuming that the demand equation for the Bike* is the same as before, what is the price that maximizes revenue for this single product and what is their new annual sales revenue? f. (2 points) Using the price from part (e) and assuming the same fixed shipping fee and annual stocking cost as before, how many Bike* units should Peloton order at each shipment? g. (8 points) Assuming that Peloton can only order once every four weeks and that the manufacturing cost of each bicycle is $500, what is the profit maximizing price? Fixed shipping fee and annual stocking cost remain the same. h. (2 points) After reviewing the historical sales data report, Peloton has realized that the analytics firm that calculated the and equation also provided a standard deviation equal to 12.5 records and if Peloton can tolerate a stockout probability of at most 5%, at what number of Bike* should they place their next order if each Bike* is priced at $2000? Recall that the lead time is 4 weeks. (Hint: Z(0.95) = 1.64.) i. (3 points) If Peloton decides to sell all three types of bicycles, the Bike at $1,500, the Bike* at $2,200, and Bike+ at $3,000 [note these numbers have changed versus the prices above], what would be Peloton's annual revenue