(Solved): Instructions - Show all work (including formulas used) for problems. No work = no credit. - You mu ...

Instructions - Show all work (including formulas used) for problems. No work = no credit. - You must use the notation (variable names, etc.) discussed in class and assigned readings. - Follow the Homework Format (see Canvas document from the beginning of the semester). - To help prepare your homework, the document Some Formulas for Homework contains formulas that can be copied and pasted. - This is an individual assignment (working with classmates is prohibited). - Originality matters! 1) A small clinic has one doctor on duty administering vaccines. Patients are served on a first-come-firstserved basis (no appointments) and the patients form a single line to wait for their vaccination. The doctor takes, on average 3 minutes to serve a patient (exponentially distributed). On average, 16 patients arrive per hour (Poisson distributed). Assume the clinic is open continuously, and that there is unlimited space for patients to wait. a) (5 points) Is this an M/M/1 system? Explain why or why not (including additional assumptions, if necessary). For parts \( b \) and \( c \), assume that it is an \( M / M / 1 \) system for purposes of calculating the answers... b) (5 points) On average, what is the total time a patient spends at the clinic? c) (5 points)) What is the average number of patients waiting in line? 2) (5 points) Based on the interview of Todd Ferris by Ellen Byron in the Wall Street Journal ("Sweet Spot .."), what is needed to be successful as a supply-chain data scientist? Do you think someone with a business degree could do this job? \( \rho=\frac{\lambda}{\mu} \quad I=1-\frac{\lambda}{\mu} \quad P_{0}=1-\frac{\lambda}{\mu} \quad P_{x}=\left(\frac{\lambda}{\mu}\right)^{2}\left(1-\frac{\lambda}{\mu}\right) \) \( W=\frac{1}{\mu-\lambda} \quad W_{s}=\frac{\lambda}{\mu(\mu-\lambda)} \quad L=\frac{\lambda}{\mu-\lambda} \quad L_{s}=\frac{\lambda}{\mu(\mu-\lambda)} \) \( T R C=\frac{A D}{Q}+\frac{h Q}{2} \) \( \operatorname{TRC}=\frac{A D}{Q}+\frac{h Q}{2}\left(1-\frac{d}{p}\right) \quad Q^{*}=\sqrt{\frac{2 A D}{h}} \quad Q^{\circ}=\sqrt{\frac{2 A D}{h\left(1-\frac{d}{p}\right)}} \) \( s=d L \) \( s=\mu_{\text {LTD }}+z \sigma_{L T D} \) \( S L=\frac{c_{2}}{c_{x}+c_{2}} \) \( \mu_{\mathrm{LTO}}=\mathrm{L}^{*} \mu_{\mathrm{d}} \quad \sigma_{\mathrm{LTO}}=\sqrt{L \sigma_{d}^{2}}=\sqrt{L} * \sigma_{\mathrm{d}} \) \( \mu_{\mathrm{LTO}}=\mu_{\mathrm{L}} * \mu_{\mathrm{d}} \quad \sigma_{\mathrm{LTD}}=\sqrt{\left(\mu_{L} * \sigma_{d}^{2}\right)+\left(\mu_{d}^{2} * \sigma_{L}^{2}\right)} \) \( U C L=\bar{x}+z \sigma_{\bar{x}} \quad L C L=\bar{x}-z \sigma_{\bar{x}} \) \( U C L=\bar{x}+A_{2} \bar{R} \quad L C L=\bar{x}-A_{2} \bar{R} \) \( U C L=D_{4} \bar{R} \quad L C L=D_{3} \bar{R} \) \( \sigma_{\bar{p}}=\sqrt{\frac{\bar{p}(1-\bar{p})}{n}} \quad U C L=\bar{p}+z \sigma_{\bar{p}} \quad L C L=\bar{p}-z \sigma_{\bar{p}} \) \( \sigma_{\bar{q}}=\sqrt{\bar{c}} \quad U C L=\bar{c}+z \sigma_{\bar{z}} \quad L C L=\bar{c}-z \sigma_{\bar{z}} \) \( C_{2}=\frac{\text { specification_width }}{6 \sigma} \)