$3\mathrm{.}15-$ 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 $($qualified graduate students$)$ are required.

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$),$ afternoon $($noon $-8$ pm$),$ and evening $(4$ pm $-$ midnight$).$ Full$-$time consultants are paid $$17\mathrm{.}50$ per hour.

Part$-$time consultants can be hired to work any of the four shifts listed in the table. Part$-$time consultants are paid $$15$ 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 may full$-$time and part$-$time consultants should work each shift to meet the above requirements at the minimum possible cost.

a $-$ Which category of linear programming problem does this problem fit? Why?

b $-$ Formulate and solve a linear programming model for this problem on a spreadsheet.

c $-$ Summarize the model in algebraic form.

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$),$ afternoon $($noon $-8$ pm$),$ and evening $(4$ pm $-$ midnight$).$ Full$-$time consultants are paid $$17\mathrm{.}50$ per hour.

Part$-$time consultants can be hired to work any of the four shifts listed in the table. Part$-$time consultants are paid $$15$ 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 may full$-$time and part$-$time consultants should work each shift to meet the above requirements at the minimum possible cost.

a $-$ Which category of linear programming problem does this problem fit? Why?

b $-$ Formulate and solve a linear programming model for this problem on a spreadsheet.

c $-$ Summarize the model in algebraic form.

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