please solve this multiple server queuing equation

we need to figure out how many employees amazon needs to hire in order to acheive a 30 minute wait period

the arrival rate is: 10

the service rate is: 975.58

the equations needed to solve this are in the picture below:

all data and info is here.

Data During the work week of April 16th, we collected data from Amazon's Tracy distribution center regarding the. Below is the data coliected: The topic of estimating how many employees Amazon needs to hire to accomplish a 30min truck wait time is a difficult queuing problem that involves the application of numerous equations. In order to answer this issue, we must utilize the arrival rate and service rate given in the problem to compute the average number of vehicles in the system and the average number of trucks waiting in line. We can then use these variables to compute the number of staff Amazon needs to hire to meet the target wait time. To determine how many employees Amazon will need to hire to achieve a 30 minute truck wait time, we need to use the multiple server queuing equation. First we need to determine the arrival rate and service rate. The arrival rate is the average time it takes for the trucks to be loaded and unloaded and the service rate is the average number of units picked up and dropped off. The arrival rate is 10 trucks per hour and the service rate is 325.2 units per hour. Arrival rate: Total number of trucks =4+3+5+9+7+3+2+4+7+6=50 Average number of trucks per hour = Total number of trucks / Number of hours Average number of trucks per hour =50/5=10 per hour Therefore, the average number of trucks per hour over a 5 - hour period is 10 Service Rate: To find the amount of units over a 5 hour day, we first need to calculate the total number of hours in 10 days: Total Hours =10 days 24 hours per day =240 hours Then we have to calculate the service rate per hour. Service rate per hour = Total units served / Total Time =78,047/240=325.2 units per hour To find the amount of units over a 5 hour day, we can simply multiply the service rate per hour by the number of hours per day: Using Littie's Law, we can calculate the average number of trucks in the system: Ls=Ws Where is the arrival rate and W is the average time trucks spend in the system. Since we want to achieve a 30 minute wait time, we can set Ws =0.5 hours Ls=100.5=5 Next, we need to determine the probability that there are no trucks in the queuing line (Po), which is given by the equation: PO=((=0c)n()n1)+(w)cxc!x(cs2)1 Where c is the number of servers, is the arrival rate, and is the service rate. Amazon has 2 servers. Next, we can use the equation for the probability that n trucks are in the system, to calculate the average number of trucks in the queue: Pn=(1/c!xc(nc))x(/)nPoforn>cPn=(1)x(/)nPofornc Pn=n1()nP0 for n