The Northside Bank is working to develop an efficient work schedule for full$-$time and part$-$time tellers $.$ The schedule must provide for efficient operation of the open from $9$:$00$ Delta$*$M to $7$:$00$ PM$.$ The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here Time No$.$ of Tellers Timeof Tellers $9$:$00$ a$.$m$,-10$:$00$ a$.$m$\mathrm{.}2$:$00$ p$,$m$,-3$:$00$ p$.$m$.10$:$00$ a$.$m$.-11$:$00$ a$.$m$.3$:$00$ n$.$m$.-4$:$00$ n$.$m $11$:$00$ a$.$m$.-$Noon $4$:$00$ n$.$m$.-5$:$00$ n$.$m$.$ Noon$-1$:$00$ p$.$m$.115$:$00$ p$,$m$.-6$:$00$ p$,$m$.1$:$00$ p$.$m$\mathrm{.}2$: $00$ p$.$m$\mathrm{.}76$:$00$ p$.$m$.-7$:$00$ p$.$m$.$ Each full$-$time employee starts on the hour and works a $4-$hour shift, followed by a $1-$hour break and then a $3-$hour shift. Part$-$ time employees work one $4-$hour bank $$15$ per hour $($$$105$ a day$),$ and part$-$time employees cost the bank per hour $($$$32$ per day$)($ a$)$ Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost $($ number of part$-$time employees coming on duty at the beginning of hour f$)$