RealCompute offers real-time computing services. The company owns 4 supercomputers that can be accessed through the internet. Their customers send jobs that arrive on average every 4 minutes (inter-arrival times are exponentially distributed and, thus, the standard deviation of the inter-arrival times is 4 minutes).
Each job takes on average 10 minutes of one of the supercomputers (during this time, the computer cannot perform any other work). Customers pay $20 for the execution of each job. Given the time-sensitive nature of the calculations, if no supercomputer is available, the job is redirected to a supercomputer of a partner company called OnComp, which charges $40 per job to Real Compute (OnComp always has supercomputer capacity available).
What is the probability with which an incoming job can be executed by one of the supercomputers owned by RealCompute?
How much does RealCompute pay on average to OnComp(in $s per hour)?