answer all in excel

1. A restaurant is open 11:30 am to 8:30 pm and requires between 6 and 12 employees depending on the time of day. The owner wants a schedule that will minimize total personnel costs. Lunch (12:30 pm to 1:30 pm) and dinner (5:30 pm to 7:30 pm) are generally the busiest. The restaurant can employ full-time or part-time employees. Part-time workers can be scheduled in 4-hour shifts and can start any time between 11:30 am and 3:30 pm. Full time workers are scheduled for the entire day and have a 1 hour lunch break, 50% eat at 2:30 pm and 50% at 3:30 pm. To encourage organizational commitment and high quality customer service, the owner wants to limit part-time employee hours to a maximum of 50% of the days total requirements. Part-timers earn $9 per hour, while a full-time employee earns $112 per day. Below are the labor requirements by hour.

Time period	Number of Employees Required
11:30 am 12:30 pm	8
12:30 pm 1:30 pm	11
1:30 pm 2:30 pm	9
2:30 pm 3:30 pm	7
3:30 pm 4:30 pm	6
4:30 pm 5:30 pm	8
5:30 pm 6:30 pm	12
6:30 pm 7:30 pm	11
7:30 pm 8:30 pm	7

Use the following to define your variables.

F = full-time employees

P₁ = part-time employees starting at 11:30 am (leaving at 3:30 pm)

P₂ = part-time employees starting at 12:30 pm (leaving at 4:30 pm)

P₃ = part-time employees starting at 1:30 pm (leaving at 5:30 pm)

P₄ = part-time employees starting at 2:30 pm (leaving at 6:30 pm)

P₅ = part-time employees starting at 3:30 pm (leaving at 7:30 pm)

1. Write the Linear Program (70 pts)
2. Solve LP Problem using Solver and write the strategy (50 pts)
3. Run a sensitivity analysis and identify the binding constraints (20 pts)
4. What is the change in the objective function value if 11:30 am to 12:30 pm needed 7 employees and 7:30 pm to 8:30 pm needed 8 employees? (20 pts)