$[0\mathrm{.}44/1$ Points$]$ ASWQUANT$1315.$E$\mathrm{.}015.$

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Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical support center and obtain free consultation.

Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution, with an arrival rate of six calls per hour. On average, it takes $7\mathrm{.}1$ minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution.

To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. $($Round your answers to four decimal places. Report time in hours.$)$

$($a$)$ What effect would the additional consultant have on customer service?

$P_0=0\mathrm{.}418$

$L_q=$

$W_q=0\mathrm{.}084$

$P_w=$

$($b$)$ Would two technical consultants enable Ocala to meet its service guidelines $($no more than $35\%$ of all customers having to wait for technical support and an average customer waiting time of two minutes or less$)?$

Two consultants $$ will $$ meet service goals with $$

$35\%$ of customers waiting an average waiting time of $$

$2$ minutes.

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