Problem 3. A dishonest developer wants to make quick money building a condominium. He sets a 1-year time table for his activities, after which he will leave town for places unknown. 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. P(x) 0.02 0.03 9 10 0.05 0.05 4 5 8 0.09 0.14 0.19 0.14 0.10 0.05 12 13 14 15 0.04 0.04 0.03 0.02 0.01 | P(x) 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