Question 2 Solve the following linear programming problem involving two variables by the graphical method. (a) Find the maximum value of the objective function Z = 4x + 6y where x 20 and y 2 0, subject to the constraints -x + y = 11 2x + 5y = 90 x + y = 27 (12 marks) ( (b) An airline offers coach and first-class tickets. For the airline to be profitable, it must sell a minimum of 25 first-class tickets and a minimum of 40 coach tickets. The company makes a profit of $225 for each coach ticket and $200 for each first-class ticket. At most, the plane has a capacity of 150 travelers. Determine how many of each ticket should be sold in order to maximize profits. Objective Function: P= 225x + 200 y Constraints: y 2 25 x240 x + ys 150 x 20 and y 20 (13 marks)