Determine the Objective Function and constraints.

JB is the director of the Computer Center for PUP. He now needs to schedule the staffing of the center. It is open from 8am til midnight. JB 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 8am-12pm 8 12pm-4pm 6 4pm-8pm 8pm-12am 10 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 (8am- 4pm), afternoon (12pm-8pm) and evening(4pm-12am). Full time consultants are paid Php 250 per hour. Part-time consultants can be hired to work any of the four shifts listed above. They are paid Php 200 per hour. An additional requirement is that during every time period, there must be at least 2 full-time consultation duty for every part-time consultant on duty. JB 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 cost. (a) Formulate a LP model for this problem and use technology to get an optimal solution to this LP using simplex algorithm. (b) If we restrict variables to be natural numbers, find an optimal solution to this LP