An insurance company offers commercial fire damage insurance to four different companies. The insurer supposes that if a fire occurs, the damage for any of the companies should be similar, following an exponential distribution with mean . Based on their different locations, each company's yearly number of fires can be modelled by a Poisson distribution with respective means 0.2, 0.3, 0.1, and 0.4. Find the moment generating function of the total loss that the insurer can expect.