Rich Moore sells Christmas trees, which he grows on his farm on the Colorado western slope. Because bad weather and heavy snow is common in December, Rich has always harvested the trees that he intends to sell in a year by December 1. Rich has been selling trees for quite a while, and he’s kept detailed records of sales in previous years. He believes the average demand for trees is 600 with a standard deviation of 100 (normal distribution).
For the coming year, Rich will sell his trees for an average price of $65 each. His cost to grow and cut each tree is estimated to be $15. Any unsold trees at the end of the season can be sold for kindling wood at a price of $5 apiece, but he will have to haul the trees to the kindling processor for an additional $1 each.
$50 revenue
$6 per piece after season (how many pieces per tree??)
a. What is the optimal number of trees that Rich should harvest to maximize his profit?
b. What is Rich’s expected profit?