1. Angelina Aniston is the Director of the Computer Center for the Pitt College. She now needs to schedule the staffing of the center. It is open from 8 am until midnight. Angelina has monitored the usage at the center at various times of the day and determined that the following numbers of computer consultants are required:
Time of Day Minimum Number of Consultants Required to be on Duty
8 AM - Noon | 6
Noon – 4 PM | 8
4 PM – 8 PM | 12
8 PM – Midnight | 6
Two types of computer consultants can be hired: full-time and part-time. The full time consultants work for eight 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 $15 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the table.
Part-time consultants are paid $11 per hour.
An additional requirement is that for each part-time consultant on duty during any time period, there must be at least two full-time consultants on duty
Angelina 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 an Linear Programming model (i.e. clearly define all variables)
b. Implement your model in a spreadsheet and solve it using Solver
c. What is the optimal solution? What is the optimal objective value?