Grading (20 pts): Your solutions should be clear and concise using appropriate mathematical notation and equation formatting. Any equations should be included on separate lines and NOT be embedded within sentences. Written responses should also be clear and concise and properly copy-edited for typos and grammatical errors prior to submission. Round Tree Resort is a hotel that provides two types of rooms Mountain View (Room Type I) and Street View (Room Type II), with three rental classes as follows: Super Saver, Deluxe, and Business Conference. The profit per night for each type of room and rental class is listed in Table A below. Note that all Business Conference customers are assigned street view rooms as these are located next to the conference center of the building. Table A: Profit per Night by Room Type and Rental Class Super Saver Deluxe Business Conference Room Type 1: Mountain View $30 $35 NA Room Type 2: Street View $20 $30 $40 Round Tree's management makes a forecast of the nightly demand by rental class for each night in the future. An optimization model should be developed to maximize profit and determine how many reservations to accept for each rental class. The average nightly demand forecast for rooms in the Summer Vacation Season is 130 rooms in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. Round Tree will not make more reservations than the forecasted amounts of each reservation for each rental class. Round Tree has a limited number of each type of room. There are 100 Mountain View Rooms and 120 Street View Rooms. The following decision variables should be used in the analysis, note that there is no B1 variable because all Business Conference attendants are assigned a street view room: Decision Variables S1 = number of Super Saver reservations taken for room type I S2 = number of Super Saver reservations taken for room type II D1 = number of Deluxe reservations taken for room type I D2 = number of Deluxe reservations taken for room type II B2 = number of Business reservations taken for room type II Prepare solutions and written responses for the questions listed below. List of Questions to Answer 1. Write out an appropriate objective function for Round Tree's optimization problem using the decision variables provided. 2. Write out the mathematical constraints that correspond to the total number of reservations that Round Tree will take for each of the three rental classes each night during the Summer Vacation Season. 3. Write out the mathematical constraints that correspond to total number of reservations Round Tree will take for each room type per night during the Summer Vacation Season. 4. Assume that the optimization model was solved and indicated the following proposed reservation policy should be used (listed below). If this reservation policy is implemented, what happens if Super Saver Demand ends up being 130 as forecasted? Proposed Solution Under Consideration: S1 = 100 S2 = 10 D1 = 0 D2 = 60 B2 = 50 Nightly Profit = $7000 5. If an existing space can be converted to create 20 additional mountain street view rooms to increase S2 from 10 to 30, would this accommodate all the forecasted demand for the Super Saver class? Please answer using either a simple Yes or No for this question. 6. Next, for the space conversion considered in question 5, calculate the corresponding increase in Nightly Profit associated with increasing S2 from 10 to per night. 30