Problem $4.$ Consider an M $/$ G $/1$ queue that serves two types of jobs: red and blue. Red jobs arrive according to a Poisson process with rate $\backslash$lambda $\_$R$=1/4$ jobs$/$sec$,$ and blue jobs arrive according to a Poisson process with rate $\backslash$lambda $\_$B$=1/2$ jobs$/$sec$.$ Red job sizes have mean $1$ and variance $1,$ whereas blue job sizes have mean $0\mathrm{.}5$ and variance $1.$ All jobs arrive to the same FCFS queue, so that, at any time, the server might be serving a red job or a blue one, and there might be jobs of one or both types in the queue. What is the mean response time of red jobs, and what is the mean response time of blue jobs?