QUESTION $2(30$ Points$)$

An inventor is looking into creating a start$-$up company based on an invention. The invention must be patented, prototyped, manufactured, and marketed; all these tasks cost money and the inventor must get a loan to cover them. The inventor has assessed the potential revenues from this venture over a period of time. The plan is to operate the start$-$up for a few years and then sell the business. In general, start$-$ups have a higher tolerance for risk, but the risk must be calculated and understood. The details are as follows:

$\backslash$table$[[,$Optimistic,Most$-$Likely,Pessimistic$],[$Patent Application Cost,$$15,000,$$$15,000,$$$15,000$