The HKUST souvenir shop is planning a new design of souvenir for the class of 2019. The shop manager has estimated the demand of the new design to be uniformly distributed over 0 and 300, DU(0,300). The shop orders each souvenir at cost w=$20 and sells it at price p=$40. Unsold souvenirs can be salvaged at values=$10. (1) Please determine the optimal stocking quantity and expected prot. (2) (Value of postponement) The shop manager is considering the option of ordering all units after the actual demand is observed, for example, by creating a waiting list for interested buyers. The unit cost of procurement with postponement is slightly higher, w'=$25. Is the postponement protable?

(3) (Tailed Postponement) To make more prots, the manager is considering tailored postponement by ordering some units at regular cost w before these selling season and more units at higher cost w' if the demand is found to be high. Please nd the optimal ordering quantity at the regular price and the optimal expected prot under tailored postponement.