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**Mppl** A guy has a chicken that gives him 10 egg/month it is known that if the eggs are not sold within a month they are no longer in good conditions to be sold. If the number of people that wants eggs per month follows a poisson distribution with mean 8 and if the guy has a profit of 7 euros for selling an egg and loses 3 if he doesn't sell if whats the expected profit per month?

How can I get the right answer? I multiplied the mean number of people that try to buy eggs by the profit of selling that amount and I got the right answer but I dont think thats a valid way of doing it or is it?