Problem 2: Consider a penalty contract with parameters (w, z). A retailer sells a certain product in a single sales season. The selling price for the product is p per unit. The demand for the product is uncertain, where D is a random variable with CDF F and pdf f) > 0. The retailer orders products from a manufacture at a wholesale price w per unit. Besides, the retailer pays the manufacture a penalty z per unit of lost sales. The manufacturer produces the product at a unit production cost c Q, the retailer pays the manufacture a penalty z per unit for lost sales. Please answer the following questions. a) Under the penalty contract (w.z), what is the shortage cost cand overage cost c for the retailer? What is the retailer's optimal order quantity QP? b) Given any order quantity Q > 0, what are the expected profits for the retailer, manufacturer, and the entire supply chain? c) Please describe the insight of the penalty contract. Explain why the penalty contract can potentially achieve supply chain coordination? d) What is the value of penalty z that allows supply chain coordination? e) Discuss a potential implementation issue for the penalty contract. Problem 2: Consider a penalty contract with parameters (w, z). A retailer sells a certain product in a single sales season. The selling price for the product is p per unit. The demand for the product is uncertain, where D is a random variable with CDF F and pdf f) > 0. The retailer orders products from a manufacture at a wholesale price w per unit. Besides, the retailer pays the manufacture a penalty z per unit of lost sales. The manufacturer produces the product at a unit production cost c Q, the retailer pays the manufacture a penalty z per unit for lost sales. Please answer the following questions. a) Under the penalty contract (w.z), what is the shortage cost cand overage cost c for the retailer? What is the retailer's optimal order quantity QP? b) Given any order quantity Q > 0, what are the expected profits for the retailer, manufacturer, and the entire supply chain? c) Please describe the insight of the penalty contract. Explain why the penalty contract can potentially achieve supply chain coordination? d) What is the value of penalty z that allows supply chain coordination? e) Discuss a potential implementation issue for the penalty contract