1. Consider the staffing problem faced by the Great Lakes Bus Company that requires the following number of drivers on each day.

Day Mon Tue Wed Thu Fri Sat Sun

Number needed 19 16 14 16 19 14 10

Each driver works for 5-consecutive days in a week and then receives two days off. The company assumes that if more than required number of drivers are scheduled to work on any given day, then the extra drivers will be given a paid day off. The company solves the following linear program to determine the optimal staffing plan

MIN Z = X1 + X2 + X3 + X4 + X5 + X6 + X7

Subject to

X1 + +X4 + X5 + X6 + X7 > 19

X1 + X2 + X5 + X6 + X7 > 16

X1 + X2 + X3 + X6 + X7 > 14

X1 + X2 + X3 + X4 + X7 > 16

X1 + X2 + X3 + X4 + X5 > 19

+ X2 + X3 + X4 + X5 + X6 > 14

X3 + X4 + X5 + X6 + X7 > 10

X1, X2, X3, X4, X5, X6, X7 > 0

Using a linear programming software, the optimal solution was found to be:

X1 = 8; X2 = 3; X3 = 0; X4 = 5; X5 = 3; X6 = 3; X7 = 0

Answer the following questions based on the above information.

1. What is the definition of the decision variables in the linear program used by the company?
2. Describe the objective function (in words) that the company uses in the linear program
3. Determine the optimal value of the objective function
4. Based on the optimal solution, how many drivers will be scheduled to work on Monday?
5. Based on the optimal solution, how many drivers will be scheduled to work on Tuesday?
   1. Suppose the drivers were paid $ 50 per weekday and $ 80 for Saturday or Sunday, What is the total money paid to the drivers if the optimal plan determined above was implemented.