A developer wants to build a condominium. His problem is to determine how many units to build. He estimates the following probabilities for the demand for his units. In the table below, x is the number of units demanded and p (x) is the probability of that demand.

The selling price for a condo unit is $100,000, while it will cost only $40,000 to build it. If the developer runs out of units while there is still demand, he charges a lost opportunity cost of $10,000. If the year passes and he has not sold all his units, he will have to dump them for $20,000 each. How many units should he build to maximize his expected profit?

.x 3 4 6 8 1 0.02 7 0.10 P (x) 0.14 0.05 2 0.03 10 0.05 . 5 0.19 13 0.03 0.09 11 0.04 9 0.14 12 0.04 14 15 0.01 p (x) 0.05 0.02