_{A firm has a monopoly on selling a patented air-purifying device. If the firm produces a units of the device, it will be able to sell these units at a price of 100-x dollars, earning a revenue of f(x) =( x ) x (100 -2) = 100.x-x2. Suppose that the number of units the firm produces is described by the random variable X, which equals 40 with probability 0.3, 50 with probability 0.6, and 60 with probability 0.1. What are the firm's expected revenues?}