The number of light bulbs of a certain type (measured in hundreds), sold by a large store during a year, is a random variable X having the distribution function

The profit that the store makes for each lightbulb sold is $1. If by the end of a year, a lightbulb has not been sold, it results in a loss of $0.2 to the store.
(i) Calculate the expected profit of the store if, at the beginning of a year, it makes an order for y hundreds of light bulbs.
(ii) What is the quantity y that the store must order in order to maximize its expected profit?

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