. RealTree, Inc. is a retailer that sells decorative trees for the holiday season. They have to place their order with the tree suppler in advance of the holiday season and they have no opportunity for resupply. Each tree costs them 25 and they sell them for 65 each. If a tree does not sell during the season, RealTree sell the wood to a paper manufacturer for 5 per tree. RealTrees owner has observed that demand is normally distributed with a mean of 1236 trees and a standard deviation of 230.

(a) How many trees should RealTrees order to maximise its expected profit?

(b) RealTrees supplier offers them the following deal: they can place a second order during the selling season (this order will be delivered just-in-time, virtually eliminating lead times), but it will cost them 30 per tree. The trees ordered before the start of the selling season will still cost 25. How many trees should RealTree order before the holiday season starts?