If you are stuck on this, don't worry! It's not meant to be easy! If you're having problems with the graph, try calculating the value of p for some values of s and plotting points. This will help you to work out the general shape of the graph.
 
When working out what optimal egg size is, try defining the function that you are attempting to maximise - the payout. In this case this is the expected number of chicks that will hatch, which is equal to the number of eggs multiplied by the probability that each egg has of survival. What is the total number of eggs equal to? How might you go about working out what the maximum of a function is? Once you've defined your function it might help to sketch a graph of it.