Question

Megan Fisher is the director of the Computer Center for Chicago College. She now needs to schedule the staffing of the center. It is open from 8 a.m. until midnight. Megan 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. to Noon 5 Noon to 4 p.m. 10 4 p.m. to 8 p. m 8 8.pm to midnight 5 Two types of computer consultants can be hired: Full time and Part time Full time consultants work for 8 consecutive hours in any of the following shifts: moining (8am to 4 pm), afternoon (Noon to 8pm) and evening (4 pm to midnight) and they are paid $30 per hour. Part time consultant can be hired to work any of the four shifts listed in above table and they are paid $20 per hour. During every time period, there must be at least 2 full time consultants on duty for every part time consultant on duty. Megan would like to determine how many full time and how many part time workers should work each shift to meet above requirements at the minimum possible cost. . .

Answer 1

As we look above we can see full time consultants need $30 per hour which is higher than part time consultant who need to pay $20 per hour.So it is good to hire more part time consultant than full time consultant but every time period there must be at least 2 full time consultants on duty for every part time consultant on duty.So the company need minimum 4 full time consultant (morning 8am-4pm and evening 4pm-midnight)

cost for full time consultant =no of full time consultant*hours each consultant work*hourly rate

=4*8*30=960

and we take part time consultant for rest no of consultant as they are cheaper than full time consultant

for 8 am to noon we need 5 minimum number of consultant so we need to hire 3 part time consultant and 2 full time consultant(needed)

for noon to 4pm we need 10 minimum number of consultant so we need to hire 8 part time consultant and 2 full time consultant(needed)

for 4 pm to 8 pm we need 8 minimum number of consultant so we need to hire 6 part time consultant and 2 full time consultant(needed)

for 8 am to noon we need 5 minimum number of consultant so we need to hire 3 part time consultant and 2 full time consultant(needed)

total cost for part time consultant=no of part time consultant*hours each consultant work*hourly rate

=20*4*20=1600

so minimum cost =960+1600=2560