$5.$ Based on Textbook problem $3\mathrm{.}4-10.$ 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 $8$ A$.$M$.$ 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:

Time of Day Minimum Number of Consultants Required to Be on Duty

$8$ A$.$M$.$noon $4$

Noon$4$ P$.$M$.8$

$4$ P$.$M$.8$ P$.$M$.10$

$8$ P$.$M$.$midnight $6$

Two types of computer consultants can be hired: full$-$time and part$-$time. The full$-$time consultants work for $8$ consecutive hours in any of the following shifts: morning $(8$ A$.$M$.4$ P$.$M$.),$ afternoon $($noon$8$ P$.$M$.),$ and evening $(4$ P$.$M$.$midnight$).$ Full$-$time consultants are paid $$40$ per hour.

Part$-$time consultants can be hired to work any of the four shifts listed in the above table. Part$-$time consultants are paid $$30$ per hour. An additional requirement is that during every time period, there must be at least $2$ full$-$time consultants on duty for every part$-$time consultant on duty.

Larry would like to determine how many full$-$time and how many part$-$time workers should work each shift to meet the above requirements at the minimum possible cost. Propose a recommended optimal solution for Larry.