Suppose you are operating a bus company. You divided a day (24 hours) into 6 equal periods and calculated how many buses will be needed in each of these periods. Below table shows the minimum number of buses required during each of these periods. 1 2 3 4 5 6 12 am - 4 am 4 am - 8 am 8 am - 12 pm 12 pm-4pm 4 pm - 8 pm 8 pm - 12 am 4 8 10 7 12 4 Periods Hours Minimum # of buses required Each bus starts to operate at the beginning of a period and operates for 2 consecutive periods in a 24-hour duration. The LP model for the above problem is given below: X = number of buses starting to operate at the beginning of period i, i = 1, 2, 3, 4, 5, 6 Min X + X + X3 + X + X5 + X6 s. t. X6 + X 4 X + X 8 X + X3 10 X3 + X 27 X + X5 12 X5 + X6 24 X 0, i 1, 2, 3, 4, 5, 6. a) (15 pts.) Find the optimal solution(s) using Excel Solver. b) (5 pts.) Are there any constraints binding? If so, which ones? c) (10 pts.) What would happen the objective function value if there are no buses starting to operate at the beginning of period 3? d) (10 pts.) What would happen the objective function value if there is a need to double the buses starting to operate at the beginning of period 2? e) (10 pts.) What would happen the objective function value if the minimum number of buses required in period 1 drops to 2? f) (10 pts.) What would happen the objective function value if the minimum number of buses required in period 5 increases to 24? g) (10 pts.) What would happen the objective function value if the minimum number of buses required in period 1 decreases by 2, in period 2 increases by 1, and in period 5 decreases by 2, at the same time? h) (10 pts.) What would happen the objective function value if the minimum number of buses required in period 1 decreases by 4, in period 6 increases by 7, at the same time?