LP Formulation The XYZ Insurance Company's regional office provides 24/7 telephone service to handle questions from its policy holders and company field agents. Service representatives work 8-hour shifts, namely: 12AM-8AM, 4AM-12AM, 8AM-4PM, 12PM-8PM, 4PM-12AM, and 8PM-4AM. Based on historical number of calls, the Management has pre-determined the staffing needs for every 4-hour time period -- as shown in the table below. Forinstance,peakhoursarefrom8AMto12PM,hencethereshouldbe10servicerepresentatives on duty during that time period.

Period	4-hour Time Period	Minimum Number of Service Representatives Needed
1	12 midnight to 4 am	2
2	4 am to 8 am	6
3	8 am to 12 noon	10
4	12 noon to 4 pm	8
5	4 pm to 8 pm	4
6	8 pm to 12 midnight	6

Required:

Formulate the LP model to determine how many service representatives should report for each shift. Show all 6 steps in model formulation. Hint #1: The more employees, The higher the cost. This info will guide you on the objective function. Hint #2: You may create a 2D table -- 8-hour shifts listed in rows, 4-hour periods listed in columns -- to visualize the variables and constraints at hand.

Optional (for Bonus Points):

Set up this model in Excel correctly, optimize, and state the optimal solution.

ii. Solving LP models through Excel Solver and Post-Optimality Analysis Suppose a linear program has the following model formulation:

Required:

Maximize Subjectto:

3X1 +5X2

X1 +X2

X2 3X1 +2X2 X1 , X2

<= 12 <= 10 <= 30 >= 0

1) Set up model and optimize using Excel Solver. Show the Answer and Sensitivity Reports. 2) Determine the optimum values of the decision variables, objective function, and limiting contraints. 3) Determine the range of values for the coefficient of X1 in the objective function over which the optimal

values of the decision variables remain unchanged. 4) Determine the range of values for the coefficient of X2 in the objective function over which the optimal

values of the decision variables remain unchanged. 5) Evaluate the shadow prices for the two limiting constraints and interpret them. Over what range of

values for the two limiting constraints are the shadow prices valid?