A Christmas tree retailer is trying to estimate demand for Christmas trees before ordering inventory for the season. The trees are purchased from the supplier for \($10\) and sold for \($25.\) Fixed costs of operating the Christmas tree lot are \($100.\) Based on prior experience, the Christmas tree retailer estimates that there is a 0.5 probability that 80 trees can be sold and a 0.5 probability that 100 trees can be sold. Any unsold trees must be discarded at a cost of \($2\) each.

a. Should the retailer order 80 or 100 trees to maximize the expected profit?

b. How would a survey that provides more precise demand for Christmas trees add value to the retailer?