A ski resort operator must decide before the winter season whether he will lease a snow-making machine. If he has no machine, he will make $20,000 if the winter is mild, $30,000 if it is typical, and $50,000 if the winter is severe. If he decides to lease the machine, his profits for these conditions will be $30,000, $35,000, and $40,000, respectively. The probability of a mild winter is 0.3, with a 0.5 chance of a typical winter and a 0.2 chance of a severe winter.
If the operator wants to maximize his expected profit, should he lease the machine? What is the most he should be willing to pay for a perfect forecast?