It's regarding operation research cost model, can you please tell me how to solve this

Question

An author has option of either publishing his novel himself or through a publisher . Publisher is offering him $ 20000$ for signing contract. If novel is successful it would Sell 20000 copies , if not then 10000 copies. Publisher pays $1$ as royalty per copy. There is 70% chance that novel will be successful. If author published himself then initially he will incur cost of $ 90000$ for printing, but each copy sold will net him $2$. Based on above info , tell which option is more beneficial

Answer 1

We could view the problem from a probabilistic point of view. In this case, earning are a random variable because we don't know how many copies are sold. Let $X=$number of copies sold, with a probability density function $$ P(X=x) = \left\{ \begin{array}{ccc} 0.3 & \text{ if } x=10~000\\ 0.7 & \text{ if } x=20~000\\ \end{array} \right. $$ In the first case, we do take the publisher deal. Now the earnings are $$ \text{Earnings}=20~000+1 \times X $$ In the second option we print the book ourselves, and the earnings are $$ \text{Earnings}=-90~000+2 \times X $$ The next step is to consider the expected value from Earnings in each case. Can you take it from here?

PS: You could also consider what happens in the "best case scenario", where sales are indeed $20~000$ copies. What's the result then?