ON EXCEL:

1. Provide the standard form (i.e., define the decision variables, objective, and all constraints mathematically) for the problem stated above.

2. Use Solver to find the minimum-cost staffing plan for the library. How many full-time staff and part-time staff will be needed for each shift? What is the minimum cost? Follow the guidelines when building the model on Excel.

3. Building upon the model created for question 2, enhance the model by making it more user-friendly by using controls (e.g., list box, spin button) so that the user can change the wage for both full-time and part-time staff and find the optimal solution. The range of the wage for fulltime staff is between $14 $20 and for part-time staff it is between $8 $13. Build this model on a separate worksheet.

4. After thinking about this problem for a while, you have decided to recognize meal breaks explicitly in the scheduling of full-time staff. In particular, full-time staff are entitled to a one hour meal break during their eight-hour shift. In addition, employment rules specify that the meal break can start after three hours of work or after four hours of work, but those are the only alternatives. Moreover, you, the director, have to determine how many full-time staff will take the meal break after three and four hours for all full-time staff. Full-time staff are paid during the meal break. Part-time staff do not receive a meal break. Provide the standard form (i.e., define the decision variables, objective, and all constraints mathematically) for this problem.

5. Use Solver to find the minimum-cost staffing plan for question 4. How many full-time consultants and part-time consultants will be needed for each shift? What is the minimum cost? Follow the guidelines when building the model on Excel.

You are the Director of the and responsible for scheduling the staff of the library, which is open from 8am until midnight. You have monitored the usage of the library at various times of the day and determined that the following of staff are required: Minimum # of staff required to be on duty Time of Day 8am noon Noon - 4pm 4pm 8pm 8pm - midnight 12 16 24 16 Two types of staff can be hired: full-time and part-time. The full-time staff work for eight consecutive hours in any of the following shifts: morning (8am - 4pm), afternoon (noon 8pm), and evening (4pm midnight). Full-time staff are paid $14 per hour. Part-time staff can be hired to work any of the four shifts listed in the table. Part-time staff are paid $12 per hour. An additional requirement is that during every time period, there must be at least one full-time staff on duty for every part-time staff on duty (e.g., if you hired three part-time staff in the noon - 4pm shift, you must have at least three full-time staff). You are the Director of the and responsible for scheduling the staff of the library, which is open from 8am until midnight. You have monitored the usage of the library at various times of the day and determined that the following of staff are required: Minimum # of staff required to be on duty Time of Day 8am noon Noon - 4pm 4pm 8pm 8pm - midnight 12 16 24 16 Two types of staff can be hired: full-time and part-time. The full-time staff work for eight consecutive hours in any of the following shifts: morning (8am - 4pm), afternoon (noon 8pm), and evening (4pm midnight). Full-time staff are paid $14 per hour. Part-time staff can be hired to work any of the four shifts listed in the table. Part-time staff are paid $12 per hour. An additional requirement is that during every time period, there must be at least one full-time staff on duty for every part-time staff on duty (e.g., if you hired three part-time staff in the noon - 4pm shift, you must have at least three full-time staff)