$4.$ Staffing Analysis $(6$:$30$ am to $1$:$30$ pm$)$:

$-$ Using the half$-$hour slots from $6$:$30$ am to $1$:$30$ pm$,$ determine the necessary staff for each slot to achieve the following goals:

$-80\%$ utilization

$-$ Less than $20$ seconds wait time

$-$ Assess whether both goals can be achieved simultaneously with the same staffing level.

$-$ Provide recommendations on whether Zappos should use different staffing goals and justify your reasoning.

$-$ Assume exponential arrival rates and a service rate $($Cs$)$ of $1\mathrm{.}25.$