JSOMAir Inc., a new airline servicing the Dallas-Cancun route, is run by JSOMs who want to make as much money as possible. JSOMAir has a new Airbus A390, and wants to know how much revenue to expect under an optimal space configuration (essentially, fare class mix).

Business class passengers require more labor from flight attendants and more physical space in the plane, but fetch a higher ticket price than Economy class passengers. The A390 is large, and can be configured flexibly to accommodate different numbers of Business and Economy class customers. However, here are the constraints:

• It has a total of 1200 net space units available for passenger use. (See table below and notice, e.g., if the space units were assigned 100% to Business class, those 1200 space units could hold 1200/2=600 Business fare passengers.)
• Also, JSOMAir labor is scarce. Only 900 labor units are available for this route. (See table below and notice, e.g., if the labor units were assigned 100% to Business class, those 900 labor units could hold 900/1.5=600 Business fare passengers.)
• The potential demand (Max Demand) is limited.
• The table below details the different contributions and requirements of each class.

Passenger Class:

Business Ticket price $1050 Flight Attendant Labor Units Required 1.5

Economy Ticket price $300 Flight Attendant Labor Units Required 1

Space Units Required 2 Max Demand 200

Space Units Required 1 Max Demand 900

Using the information above, formulate JSOMAir's space configuration decision as a linear programming.

a) (8 points) Using the information above, formulate JSOMAir's space configuration decision as a linear programming.

Objective function and constraints

b) (10 points) Solve the linear programming using the iso profit line method. In the picture, clearly identify the feasible region and the best isoprofit line.

Graph

optimal solution

optimal objective value

Note: Problems (c), (d), and (e) have independent assumptions. For example, when working on (e), you do not need to consider the assumptions made in (c) or (d).When necessary, use the graph you draw in part (b) to explain your argument.

c) (4 points) Thanks to the high popularity of Cancun, the price of Economy class tickets increases (with maximum demand unchanged). How much does the ticket price need to increase so that it is optimal for JSOMAir to serve only Economy class?

d) (4 points) JSOMAir has a contract with FedEx to lease the space on the plane at a price of $100 per space unit. How many space units should JSOMAir lease to FedEx?

e) (4 points) JSOMAir is considering hiring more flight attendants. One additional attendant provides 150 additional labor units. How much JSOMAir is willing to pay for one additional attendant (per trip)?