Using the table, first write the objective function. Notice that from 4:00PM to 8:00PM, both day-shift and night-shift workers are working and each period is 4-hour long.
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Let x be the number of day-shift workers and let y be the number of night-shirt workers.
Time
noon to 4:00PM
4:00PM to 8:00PM
8:00PM to midnight
Number of Employees Needed
at least 5
at least 14
6
Rate per hour
$5.50
$7.50
$7.50
Let C be the total cost. Looking at the table, we will first write the objective function. Notice that from 4:00PM to 8:00PM, both day-shift and night-shift workers are working and each period is 4-hour long.
Verbal Expression
Algebraic Expression
Cost of x workers that work from noon to 4:00PM
5.50(4) x
Cost of ( x+ y) workers that work from 4:00PM to 8:00PM
7.50(4)( x+ y)
Cost of y workers that work from 8:00PM to midnight
7.50(4) y
Total cost is $C.
C=5.50(4) x+7.50(4)( x+ y)+7.50(4) y
Let's simplify the equation before we find the minimum cost.
To minimize the cost, we should schedule minimum number of workers. Therefore, the minimum number of night-shift workers will be 6. Because the number of workers that work from 4:00PM to 8:00PM is at least 14, we can say that the number of day-shift workers is 8.
