The university's Library Services Department is planning to upgrade its online research assistanceprogram. The program provides live chat support to students seeking help with research, accessingdatabases, and utilizing library resources effectively. Currently, the service operates with oneassistant $24/7.$ The university is contemplating adjustments to optimize this service.Historical data has provided the following discrete probability distribution for the time $($in minutes$)$a research assistant spends assisting a student:Assistance Time $($min$)$ Probability$50\mathrm{.}20100\mathrm{.}35150\mathrm{.}25200\mathrm{.}20$Student queries arrive according to the following discrete distribution:Interarrival Time $($min$)$ Probability$30\mathrm{.}2550\mathrm{.}3070\mathrm{.}2090\mathrm{.}15110\mathrm{.}10$The university estimates the value of students' time at $$10$ per hour. A research assistant's wage is$$20$ per $4-$hour shift. The Library Services Department covers the cost of the research assistants.Questions for Analysis:$1.$ Cost Analysis with Current Staffing: Assuming the current staffing levels $($two assistantsduring peak hours and one during off$-$peak hours$),$ calculate the total operational cost perday. This cost includes the value of students' time waiting and the wages of the researchassistants$\mathrm{.}2.$ Staff Utilization and Idle Time: Determine the research assistants' idle time percentageand utilization rate during both peak and off$-$peak hours$\mathrm{.}3.$ Evaluating Staffing Adjustments: Based on your analysis, would you recommend anychanges to the number of research assistants during peak and off$-$peak hours? Justify yourrecommendation with cost and efficiency considerations$\mathrm{.}4.$ Optimal Staffing Strategy: What is the optimal number of research assistants to minimizethe total operational cost while maintaining a high level of service? Consider differentscenarios for peak and off$-$peak hours.Task: Simulate the system for at least $50$ arrivals during both peak and off$-$peak periods tounderpin your analysis and recommendations.

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Incude execl sheet in solution.