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. 14 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 $52 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 parttime 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. Formulate a linear programming model for this problem. Let f1 = number of full-time consultants working the morning shift (8 a.m.-4 p.m.), f2 = number of full-time consultants working the afternoon shift (Noon-8 p.m.), f3 = number of full-time consultants working the evening shift (4 p.m.-midnight), p1 = number of part-time consultants working the first shift (8 a.m.-noon), p2 = number of part-time consultants working the second shift (Noon-4 p.m.), p3 = number of part-time consultants working the third shift (4 p.m.-8 p.m.), p4 = number of part-time consultants working the fourth shift (8 p.m.-midnight). QUESTIONS: fill in blank with options provided _________ ( maximize , minimize) C = _________ (30 x 4, 52 x 8, 30 x 8, 52 x 4, f1 + f2 + f3) + ________ (30 x 4, 30 x 8, 52 x 4, 52 x 8, p1 + p2 + p3 + p4) subject to ___________ (f1 + f2 + f3+ p3 ≥ 14, f1 + f2 ≥ 4, f1 + p1 ≥ 4, f3 + p4 ≥ 10 ) _____________ (f3 + p3 ≥ 6, f1 + f2 + p2 ≥ 14, f1 + p1 ≥ 10, f1 + f3 + p3 ≥ 14) ______________ (f2 + f4 + p3 ≥ 14, f3 + f4 + p3 ≥ 10, f2 + f3 + p3 ≥ 10, f2 + f3 + p3 ≥ 14) ______________ (f3 + f4 ≥ 14, f3 + f4 ≥ 6, f2 + f3 + p3 ≥ 6, f3 + p4 ≥ 6) f1 ≥ 2p1 f1 + f2 ≥ 2p2 f2 + f3 ≥ 2p3 f3 ≥ 2p4 f1, f2, f3, p1, p2, p3, p4 ≥ 0
Larry Edison is the director of the Computer Center for Buckly College. He now needs to
| Time of Day | Minimum Number of Consultants Required to Be on Duty |
| 8 A.M.–noon | 4 |
| Noon–4 P.M. | 14 |
| 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 $52 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 parttime 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.
Formulate a linear programming model for this problem.
Let f1 = number of full-time consultants working the morning shift (8 a.m.-4 p.m.),
f2 = number of full-time consultants working the afternoon shift (Noon-8 p.m.),
f3 = number of full-time consultants working the evening shift (4 p.m.-midnight),
p1 = number of part-time consultants working the first shift (8 a.m.-noon),
p2 = number of part-time consultants working the second shift (Noon-4 p.m.),
p3 = number of part-time consultants working the third shift (4 p.m.-8 p.m.),
p4 = number of part-time consultants working the fourth shift (8 p.m.-midnight).
QUESTIONS: fill in blank with options provided
_________ ( maximize , minimize) C = _________ (30 x 4, 52 x 8, 30 x 8, 52 x 4, f1 + f2 + f3) + ________ (30 x 4, 30 x 8, 52 x 4, 52 x 8, p1 + p2 + p3 + p4)
subject to ___________ (f1 + f2 + f3+ p3 ≥ 14, f1 + f2 ≥ 4, f1 + p1 ≥ 4, f3 + p4 ≥ 10 )
_____________ (f3 + p3 ≥ 6, f1 + f2 + p2 ≥ 14, f1 + p1 ≥ 10, f1 + f3 + p3 ≥ 14)
______________ (f2 + f4 + p3 ≥ 14, f3 + f4 + p3 ≥ 10, f2 + f3 + p3 ≥ 10, f2 + f3 + p3 ≥ 14)
______________ (f3 + f4 ≥ 14, f3 + f4 ≥ 6, f2 + f3 + p3 ≥ 6, f3 + p4 ≥ 6)
f1 ≥ 2p1
f1 + f2 ≥ 2p2
f2 + f3 ≥ 2p3
f3 ≥ 2p4
f1, f2, f3, p1, p2, p3, p4 ≥ 0
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