Question 1170863
This is a classic linear programming problem, but with some extra constraints and calculations. Let's break down each part of the analysis.

**1. Minimizing Total Daily Cost**

This part requires setting up and solving a linear programming model.

**Variables:**

* DT_A: Number of 2-hour part-timers in Downtown (DT)
* DT_B: Number of 4-hour part-timers in DT
* DT_C: Number of 8-hour full-timers in DT
* RA_A: Number of 2-hour part-timers in Residential Area (RA)
* RA_B: Number of 4-hour part-timers in RA
* RA_C: Number of 8-hour full-timers in RA
* TA_A: Number of 2-hour part-timers in Touristic Area (TA)
* TA_B: Number of 4-hour part-timers in TA
* TA_C: Number of 8-hour full-timers in TA

**Objective Function (Minimize Total Cost):**

Minimize Z = 16(DT_A) + 14(DT_B) + 12(DT_C) + 10.5(RA_A) + 9.5(RA_B) + 8(RA_C) + 12(TA_A) + 11(TA_B) + 9(TA_C)

**Constraints:**

* **Employee Availability:**
    * DT_A + RA_A + TA_A <= 30 (2-hour part-timers)
    * DT_B + RA_B + TA_B <= 35 (4-hour part-timers)
    * DT_C + RA_C + TA_C <= 15 (8-hour full-timers)
* **Hourly Employee Requirements (for each branch and each hour):**
    * **DT:**
        * 12pm-1pm: DT_C >= 12
        * 1pm-2pm: DT_C >= 12
        * 2pm-3pm: DT_C >= 11
        * 3pm-4pm: DT_C >= 9
        * 4pm-5pm: DT_B + DT_C >= 7
        * 5pm-6pm: DT_A + DT_B + DT_C >= 6
        * 6pm-7pm: DT_A + DT_B + DT_C >= 6
        * 7pm-8pm: DT_A + DT_B + DT_C >= 5
        * 8pm-9pm: DT_A + DT_B + DT_C >= 5
        * 9pm-10pm: DT_A + DT_B + DT_C >= 4
    * **RA:**
        * 12pm-1pm: RA_C >= 9
        * 1pm-2pm: RA_C >= 9
        * 2pm-3pm: RA_C >= 8
        * 3pm-4pm: RA_C >= 8
        * 4pm-5pm: RA_B + RA_C >= 9
        * 5pm-6pm: RA_A + RA_B + RA_C >= 10
        * 6pm-7pm: RA_A + RA_B + RA_C >= 10
        * 7pm-8pm: RA_A + RA_B + RA_C >= 11
        * 8pm-9pm: RA_A + RA_B + RA_C >= 9
        * 9pm-10pm: RA_A + RA_B + RA_C >= 7
    * **TA:**
        * 12pm-1pm: TA_C >= 5
        * 1pm-2pm: TA_C >= 5
        * 2pm-3pm: TA_C >= 6
        * 3pm-4pm: TA_C >= 6
        * 4pm-5pm: TA_B + TA_C >= 8
        * 5pm-6pm: TA_A + TA_B + TA_C >= 8
        * 6pm-7pm: TA_A + TA_B + TA_C >= 10
        * 7pm-8pm: TA_A + TA_B + TA_C >= 12
        * 8pm-9pm: TA_A + TA_B + TA_C >= 12
        * 9pm-10pm: TA_A + TA_B + TA_C >= 10
* **End of Day Full-Time Constraint:**
    * DT_C >= 1
    * RA_C >= 1
    * TA_C >= 1
* **Non-negativity:**
    * All variables >= 0

**Solving this Linear Program:**

This requires using a linear programming solver (like Excel Solver, Python's `scipy.optimize.linprog`, or a dedicated LP software).

**2. Extra Employee Hours**

Once the optimal solution is found, calculate the extra employee hours for each hour in each branch. For example, if the model says DT_C = 13, and the requirement for 12pm-1pm is 12, then there is one extra employee-hour.

**3. Savings with 5 More Full-Time Employees**

* Increase the constraint for full-time employees: DT_C + RA_C + TA_C <= 20
* Re-solve the linear program.
* Calculate the difference in the total cost between the original solution and the new solution.

**4. Branch Costing Most for End-of-Day Policy**

* Examine the optimal solution and determine which branch has the highest cost associated with its full-time employees (DT_C, RA_C, TA_C). Multiply the number of full time employees in each branch by the cost per hour, and then by 8. Then compare the results.

**Important Notes:**

* This problem requires a linear programming solver.
* The results will depend on the optimal solution found by the solver.
* The exact numbers will depend on the solver, but this process will provide the solution.