Almighty Inn is a local hotel that provides three types of rooms (based on size) with...

 

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Almighty Inn is a local hotel that provides three types of rooms (based on size) with two rental classes (based on room decoration and amenities). The following table shows the profit per night for each type of room and rental class: Room Type Type-I Type-II Type-III Rental Type Super Saver $60 $75 $90 Deluxe $100 $130 Type-I rooms are too small and have a weak WiFi signal, therefore they are not eligible to be prepared for the deluxe rental class. At the Newport Beach location, Almighty has 300 Type-1, 400 Type-II, and 200 Type-III rooms available. The maximum demand forecast for a particular night is 500 rentals in the Super Saver class, 300 rentals in the Deluxe class. a) Formulate a Linear Program that determines how many reservations from each rental class should be accepted and fulfilled on which room type so as to maximize profit on that particular night, while making sure that the maximum demand and the availability of different room types are not exceeded. Clearly define your decision variables, and write the objective function and constraints in algebraic form. b) Use Excel solver to model and solve the problem. What is the optimal solution and what are the binding constraints? Provide a screenshot of your Answer Report. c) Provide a screenshot of a Sensitivity Report and base your answers to the following questions on this report. In each of the following scenarios, assume all other parameters remain unchanged. Determine whether the optimal solution and/or the objective function value (profit) will change, and if so, calculate the amount of change if possible: 1. Supersaver rentals could be rented at $85 in Type-II rooms, instead of $75. 2. The demand for Supersaver rentals was increased by 30. 3. The demand for Deluxe rentals was decreased by 10. d) Are any Type III room rented at the Supersaver price part of the current optimal solution? If not, what is the minimum Supersaver price for Type III room under which it is optimal to rent some of this type of rooms for Supersaver customers (assuming all other parameters remain the same)? e) Suppose that a small office could be converted to a Type II rental room at $50. Would you recommend doing this? Why? Almighty Inn is a local hotel that provides three types of rooms (based on size) with two rental classes (based on room decoration and amenities). The following table shows the profit per night for each type of room and rental class: Room Type Type-I Type-II Type-III Rental Type Super Saver $60 $75 $90 Deluxe $100 $130 Type-I rooms are too small and have a weak WiFi signal, therefore they are not eligible to be prepared for the deluxe rental class. At the Newport Beach location, Almighty has 300 Type-1, 400 Type-II, and 200 Type-III rooms available. The maximum demand forecast for a particular night is 500 rentals in the Super Saver class, 300 rentals in the Deluxe class. a) Formulate a Linear Program that determines how many reservations from each rental class should be accepted and fulfilled on which room type so as to maximize profit on that particular night, while making sure that the maximum demand and the availability of different room types are not exceeded. Clearly define your decision variables, and write the objective function and constraints in algebraic form. b) Use Excel solver to model and solve the problem. What is the optimal solution and what are the binding constraints? Provide a screenshot of your Answer Report. c) Provide a screenshot of a Sensitivity Report and base your answers to the following questions on this report. In each of the following scenarios, assume all other parameters remain unchanged. Determine whether the optimal solution and/or the objective function value (profit) will change, and if so, calculate the amount of change if possible: 1. Supersaver rentals could be rented at $85 in Type-II rooms, instead of $75. 2. The demand for Supersaver rentals was increased by 30. 3. The demand for Deluxe rentals was decreased by 10. d) Are any Type III room rented at the Supersaver price part of the current optimal solution? If not, what is the minimum Supersaver price for Type III room under which it is optimal to rent some of this type of rooms for Supersaver customers (assuming all other parameters remain the same)? e) Suppose that a small office could be converted to a Type II rental room at $50. Would you recommend doing this? Why?

Answer rating: 100% (QA)

a Formulation of the Linear Program Lets define the decision variables Let xij represent the number of reservations from rental class i Super Saver or ... View the full answer