Bob White is a senior engineer at AirCoach. Now they are designing a new passenger aircraft and Bob is responsible for optimizing the seat plan. Bob has to decide the numbers of the economy-class seats and the business-class seats, respectively. The total area for passenger seats is 1,000 units. Each economy-class seat takes 5 units of space and each business-class seat takes 9 units of space. For the entire life cycle of the plane, each economy-class seat can generate a total profit of $250,000 on average and each business-class seat can generate a total profit of $800,000 on average. To make sure that airlines can break even on average, the design has to meet the target that the expected total profit (without subtracting the cost of buying the plane) over the entire life cycle of the plane is at least $80,000,000, which is the listed price of the plane. Besides, due to the restriction on the total weight of the plane, the total number of seats cannot exceed 120. According to historical data, an economy-class seat is used 95% of the time on average and a business-class seat is used 70% of the time on average. The goal of Bob is to maximize the average passenger load of the plane; in other words, the objective is to maximize 0.95X + 0.7Y, where X is the number of economy-class seats and Y is the number of business-class seats. Bob formulated and solved the problem in Excel, and obtain the following output table for sensitivity analysis.Variable Cells Final Objective Allowable Allowable Cell Name Value Coefficient Increase Decrease SD$5 # of seats Economy 29.09090909 0.95 infinity 0.25 SESS # of seats Business 90.90909091 0.7 0.25 infinity Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$5 # of seats 120 1.063636364 120 11.42857143 20 SG$6 space 963.6363636 0 1000 infinity 36.36363636 SG$7 profit 80000000 -0.00000045 80000000 5000000 50000000 (a) If Bob decides to round the optimal solution to the nearest integer, then what are the optimal numbers of economy-class and business-class seats? (5 points) (b) If the listed price of the plane is reduced by $6,000,000, how would the change affect the optimal average passenger load of the plane? (5 points) (c) Plot the feasible region and solve out all the corner points. (10 points)