Consider the host$/$seater job in a full$-$service restaurant. Suppose that it takes an average of $2\mathrm{.}5$ minutes to greet a group of customers, check their reservation, and seat them. The expected number of new groups arriving during each hour on a particular day is given below.

Time period Noon$1$ p$.$m$.12$ p$.$m$.23$ p$.$m$.34$ p$.$m$.45$ p$.$m$.56$ p$.$m$.67$ p$.$m$.78$ p$.$m$.89$ p$.$m$.910$ p$.$m$.1011$ p$.$m$.11$ p$.$m$.$Midnight

No$.$ of new groups $20602081414403050403014$

a$.$ Determine the number of hosts$/$seaters required during each hour. Round up if the number has a decimal. $($Hint: You don$$t need more than three hosts$/$seaters for any hour.$)$

b$.$ Schedule three$-$ to eight$-$hour$-$long shifts to cover the host$/$seater requirements you derived in part a$.$ Use the shift scheduling heuristic. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$