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Check My Work $(1$ remaining$)$

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 bank, including adequate customer service, employee breaks, and so on$.$ On Fridays, the bank is open from $9$:$00$ A$.$M$.$ to $7$:$00$ P$.$M$.$ The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here.

Time No$.$ of Tellers Time No$.$ of Tellers

$9$:$00$ a$.$m$.-10$:$00$ a$.$m$.52$:$00$ p$.$m$.-3$:$00$ p$.$m$.8$

$10$:$00$ a$.$m$.-11$:$00$ a$.$m$.33$:$00$ p$.$m$.-4$:$00$ p$.$m$.4$

$11$:$00$ a$.$m$.-$Noon $104$:$00$ p$.$m$.-5$:$00$ p$.$m$.8$

Noon$-1$:$00$ p$.$m$.95$:$00$ p$.$m$.-6$:$00$ p$.$m$.8$

$1$:$00$ p$.$m$.-2$:$00$ p$.$m$.106$:$00$ p$.$m$.-7$:$00$ p$.$m$.4$

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 shift beginning on the hour. Considering salary and fringe benefits, full$-$time employees cost the bank $$15$ per hour $($$$105$ a day$),$ and part$-$time employees cost the bank $$8$ per hour $($$$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. $($Hint: Let xi $=$ number of full$-$time employees coming on duty at the beginning of hour i and yj $=$ number of part$-$time employees coming on duty at the beginning of hour j$.)$

If your answer is zero enter $0$ and if the constant is $"1"$ it must be entered in the box.