$$

$330$

CHAPTER $8*$ LINEAR PROGRAMMING APPLICATIONS

$8-3($Restaurant work scheduling problem$)$ The famous Y$.$ S$.$ Chang Restaurant is open $24$ hours a day. Waiters and busboys report for duty at $3$ A$.$M$.,7$ A$.$M$.,11$ A$.$M$.,3$ P$.$M$.,7$ P$.$M$.,$ or $11$ P$.$M$.,$ and each works an $8-$hour shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided. Chang's scheduling problem is to determine how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day's operation. $($Hint: Let $x_i$ equal the number of waiters and busboys beginning work in time period $i,$ where $i=1,2,3,4,5,6.)$

$\backslash$table$[[$PERIOD$,$TIME,$\backslash$table$[[$NUMBER OF WAITERS$],[$AND BUSBOYS REQUIRED$]]],[1,3$ A$.$M$.-7$ A$.$M$.,3],[2,7$ A$.$M$.-11$ A$.$M$.,12],[3,11$ A$.$M$.-3$ P$.$M$.,16],[4,3$ P$.$M$.-7$ P$.$M$.,9],[5,7$ P$.$M$.-11$ P$.$M$.,11],[6,11$ P$.$M$.-3$ A$.$M$.,4]$ how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day's operation