George and Jane are thinking of introducing three reservation packages: Standard, Deluxe and Premium. Guests who choose a Deluxe package would be entitles to a free breakfast and have priority access to the newly installed wood fired spa. A Premium package would also include a free breakfast and priority access to the spa, plus a free wine tour. With 6 treehouses in total and assuming full occupancy, the maximum number of bookings per month is 180. Based on estimated demand, George and Jane would expect at most 150 Standard reservations per month, and a maximum of 30 Premium reservations per month. They would like to limit the total number of Deluxe and Premium reservations to 60. Each Standard reservation is expected to generate a profit of $25. Profits per night for Deluxe and Premium reservations are $35 and $40, respectively. George and Jane interested in maximising the monthly profit. (a) (4 marks) Formulate a linear programming model for The Treetop Retreat. In doing so, clearly indicate the following: What are the decision variables? Define them precisely. What is the objective? Using your decision variables, formulate the objective function. What are the constraints? Using your decision variables, formulate these constraints. (b) (3 marks) Use EXCEL Solver to obtain a solution to the linear programming model from part (a), together with an Answer Report and a Sensitivity Report. Provide a copy of your EXCEL spreadsheet and of the two Solver reports in this Appendix. EXCEL Instructions: All EXCEL output should bear your e-mail ID. To ensure this, you will need to save your EXCEL file as 'E-mail ID The Treetop Retreat.xlsx' BEFORE you run Solver. In addition, your constraint names should begin with your initials, eg MK Total bookings. Refer to Activity 4D and 4E for detailed instructions on how to set up your spreadsheet and use Solver. You can set up your own spreadsheet, or use the LP Solver template, available from the course learnooline website. (c) (3 marks) Suppose that the profit per Premium reservation turns out to be $38 instead of $40. Would the solution obtained in part (b) still be optimal? Which of the Solver reports helps you answer this question and how? How would the solution change, if at all? Explain briefly and include a copy of your new Answer Report ONLY, if needed to describe the outcome of the proposed change. (d) (3 marks) Return all parameters to their values from part (b). What if the profit per Deluxe reservation turns out to be $45 instead of $35? Would the solution obtained in part (b) still be optimal? Which of the Solver reports helps you answer this question and how? How would the solution change, if at all? Explain briefly and include a copy of your new Answer Report ONLY, if needed to describe the outcome of the proposed change. (e) (3 marks) Return all parameters to their values from part (b). Suppose that The Treetop Retreat increases the limit on Deluxe and Premium packages combined to 80. Would the solution obtained in part (b) still be optimal? Which of the Solver reports helps you answer this question and how? Explain briefly and attach your new Answer Report ONLY, if needed to describe the outcome of the proposed change.