At the start of the COVID crisis one of its vendors contacts House Depot and offers to sell a large quantity of hand sanitizer. The vendor will charge House Depot $100 per case. House Depot estimates that the sanitizer shortage will last 3 months, and that whatever sanitizer is left unsold after these three months will be simply given away. a. House Depot estimates that if it retails the sanitizer at the equivalent of $300 per case, the demand for the sanitizer during the shortage period will be uniformly distributed between 500 and 800 cases. What order quantity (# of cases) would maximize House Depot's expected profit? Show your calculations. (1 pt) b. If House Depot orders the quantity you recommended in part (a), what will be the probability that there will be some amount of sanitizer that will have to be simply given away? (1 pt) C. Another option that House Depot considers is to sell the sanitizer at $200 per case. In that case, the demand during the shortage period is estimated to be uniformly distributed between 550 and 850 cases. Assuming House Depot wants to maximize its expected profit, what action would you recommend to House Depot: setting the retail price at $300 per case as in (a) or at $200 per case? Explain your reasoning, and show your calculations (3 pts) d. Assuming House Depot went with your recommendation in part (c), is House Depot guaranteed to make a larger profit than if it went with the other retail pricing choice? Explain your answer -- two sentences maximum! (1 pt) At the start of the COVID crisis one of its vendors contacts House Depot and offers to sell a large quantity of hand sanitizer. The vendor will charge House Depot $100 per case. House Depot estimates that the sanitizer shortage will last 3 months, and that whatever sanitizer is left unsold after these three months will be simply given away. a. House Depot estimates that if it retails the sanitizer at the equivalent of $300 per case, the demand for the sanitizer during the shortage period will be uniformly distributed between 500 and 800 cases. What order quantity (# of cases) would maximize House Depot's expected profit? Show your calculations. (1 pt) b. If House Depot orders the quantity you recommended in part (a), what will be the probability that there will be some amount of sanitizer that will have to be simply given away? (1 pt) C. Another option that House Depot considers is to sell the sanitizer at $200 per case. In that case, the demand during the shortage period is estimated to be uniformly distributed between 550 and 850 cases. Assuming House Depot wants to maximize its expected profit, what action would you recommend to House Depot: setting the retail price at $300 per case as in (a) or at $200 per case? Explain your reasoning, and show your calculations (3 pts) d. Assuming House Depot went with your recommendation in part (c), is House Depot guaranteed to make a larger profit than if it went with the other retail pricing choice? Explain your answer -- two sentences maximum! (1 pt)
