A hotel provides two types of rooms, Type A and Type B, with different prices depending on four distinct room classes: standard, deluxe, suite, and business. The price per night for each type of room and room class is as follows: Room class Deluxe Business Standard Suite Room Type A Type B $85 $100 $100 $120 $115 $145 $180 Type A rooms are not available for the business class. The hotel has a demand forecasting system for rooms for future nights and aims to maximize revenue by determining the optimal number of reservations to accept for each type and class of rooms. The demand forecast for a specific night indicates a demand of 100 standard rooms, 140 deluxe rooms, 120 suite rooms, and 70 business rooms. The hotel has a total of 180 Type A rooms and 220 Type B rooms. The manger notices that the hotel cannot meet all demands. (Data file (excel) can be downloaded from Brightspace). 1) Formulate the problem as a linear programming. Clear define decision variable(s), objective function, and constraints by presenting the conceptual model (see the instruction above in red). Requirement: for the conceptual model, the objective function and constraints should clearly show mathematical relationships. 2) Develop an Excel model to determine how the hotel's manager should allocate the room, and provide your answer. Which demand by class of rooms cannot be satisfied? 3) With a little work, an unused office area could be converted to a room. If the conversion cost is the same for both types of rooms, clearly provide solution map indicating the additional constraint(s) that should be included or the constraint(s) that should be changed in order to provide a recommendation on whether the hotel should convert the office to a Type A or Type B room.