(Selling Grills) Smith and Jackson Inc. (SJ) sells an outdoor grill to Cusano's Hardware Store. SJ's wholesale price for the grill is $185. (The wholesale price includes the cost of shipping the grill to Cusano). Cusano sells the grill for $250 and SJ's variable cost per grill is $100. Suppose Cusano's forecast for season sales can be described with a Poisson distribution with mean 8.75 . Furthermore, Cusano plans to make only one grill buy for the season. Grills left over at the end of the season are sold at a 75 percent discount. a. How many grills should Cusano order? [19.3] b. What is Cusano's expected profit given Cusano's order in part a? [19.3] c. What is SJ's expected profit given Cusano's order in part a? [19.3] d. To maximize the supply chain's total profit (SJ's profit plus Cusano's profit), how many grills should be shipped to Cusano's Hardware? [19.3] Suppose SJ were to accept unsold grills at the end of the season. Cusano would incur a \$15 shipping cost per grill returned to SJ. Among the returned grills, 45 percent of them are damaged and SJ cannot resell them the following season, but the remaining 55 percent can be resold to some retailer for the full wholesale price of $185. e. Given the possibility of returning grills to SJ, how many grills should be sent to Cusano's to maximize the supply chain's total profit? [19.4] Suppose SJ gives Cusano a 90 percent credit for each returned grill; that is, SJ pays Cusano $166.50 for each returned grill. Cusano still incurs a $15 cost to ship each grill back to SJ. f. How many grills should Cusano order to maximize his profit? [19.4] g. What is Cusano's expected profit given Cusano's order in part f? [19.4] h. What is SJ's expected profit given Cusano's order in part f? [19.4] i. To maximize the supply chain's total profit, what should SJ's credit percentage be? (The current credit is 90 percent.) [19.4] Dave Luna, the director of marketing and sales at SJ, suggests yet another arrangement. He suggests that SJ offer an advanced purchase discount. His plan works as follows: There is a 10 percent discount on any grill purchased before the season starts (the prebook order), but then retailers are able to purchase additional grills as needed during the season at the regular wholesale price (at-once orders). With this plan, retailers are responsible for selling any excess grills at the end of the season; that is, SJ will not accept returns. Assume SJ makes enough grills to satisfy Cusano's demand during the season and any leftover grills can be sold the next season at full price. j. Given this advanced purchase discount plan, how many grills should Cusano prebook to maximize his profit? [19.5] k. What is Cusano's expected profit given Cusano's prebook order quantity in part j? [19.5] 1. What is SJ's expected profit from sales to Cusano this season given Cusano's prebook order quantity in part j ? [19.5] m. As a thought experiment, which one of these contractual arrangements would you recommend to SJ? [19.5]