Larry Edison is the Director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 AM until midnight. Larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required:
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Time of Day
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Minimum Number of Consultants Required to be on Duty
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|
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8 AM -noon
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4
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Noon - 4 PM
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8
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4 PM - 8 PM
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10
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8 PM - Midnight
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6
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Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecutive hours in any of the following shifts: morning (8 AM - 4 PM), and evening (4 PM - Midnight). Full-time consultants are paid $14.00 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12.00 per hour.
An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty.
Larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost.
a-Formulate a linear programming model for this problem on a spreadsheet. Use the Solver to solve this model.
b-Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints.