Question $2.(43$ pts$)$ UA$$s Yummy Cafeteria offers grab$-$and$-$go lunch options, including vegetarian and gluten$-$free $($GF$)$ options. Upon arrival, each student looks at the daily menu and decides whether to eat at the cafeteria or leave $($this takes a negligible amount of time, hence there is no waiting for this step$).$ The cafeteria is organized into three sections: general section $($for those with no dietary restriction$),$ vegetarian section, and GF section. There are two payment options: cashier and the automated payment system. Around $70\%$ in the general section use the cashier, and $30\%$ use the automated system; around $80\%$ in the vegetarian section use the cashier, and $20\%$ use the automated system; and around $60\%$ in the GF section use the cashier, and $40\%$ use the automated system. In system represents the inventory $($i$.$e$.,$ the number of students in each section$).$

$($a$)[4$pts$]$ Determine the number of students per hour that:

buy lunch from the general section $=$ buy lunch from the vegetarian section $=$ buy lunch from the GF section $=$

leave the cafeteria and eat elsewhere $=$

$($b$)[10$pts$]$ Determine the number of students per hour that visit each path:

daily menu $-$ general $-$ cashier $=$

daily menu $-$ general $-$ automated payment $=$

daily menu $-$ vegetarian $-$ cashier $=$

daily menu $-$ vegetarian $-$ automated payment $=$

daily menu $-$ GF $-$ cashier $=$

daily menu $-$ GF $-$ automated payment $=$

throughput per hour$=$

$($c$)[9$pts$]$ Determine the flow time for $($write the time unit$)$:

daily menu check $=$

general section $=$

vegetarian section $=$

GF section $=$

other restaurant$=$

$($d$)[15$ pts$]$ Determine the time until $($write the time unit$)$ CLEARLY SHOW ALL YOUR WORK: cashier $=$

automated payment $=$

other restaurant $=$

$($e$)[5$pts$]$ To verify your answer in part $($d$),$ determine the flow time in the system

T$\_$sys

Show that the calculated flow times until the cashier and the automated payment in part $($d$)$ are correct