I need these six equations written to work in a c++ code.

A sample input and output for each equation:

An Analytical Model of typical Queue measures Analytical models can be computed a-priori to predict the functioning of a system. There is a convenient set of formulas that will give you the results you would expect to see the long run in a simulation. Your computer modeling will vary to some degree from the data points provided by these equations since the equations are based on large populations. 1. The percent idle time, Po; that is, the percentage of time that no one is in the system: P0=[i=0i=M1i!1()i]+M!1(^)MMM1 2. The average number of people in the system (the number in line plus the number being served. L=(M1)!(M)2(/)MP0+ 3. The average time a customer spends in the system. (the time the customer spent in line plus the time spent getting service): W=(M1)!(M)2(/)MP0+1=L 4. The average numbers of customers in the queue: Lq=L 5. The average time a customer spends waiting in the queue: wq=w1=Lq 6. The utilization factor for the system, (rho); that is, the proportion of the system's resources which is used by the traffic which arrives. =M When your program runs, you will compute and display all six values from the Analytical Model. Example input and results: The analytical model should produce these results for the following inputs: - lambda()=2 - mu()=3 - M=2 Po=0.5L=0.75W=0.375Lq=0.083Wq=0.0417