Problem Solving Question I $[$Total $27$ points$]$ A cruise ship offers two types of cabins, Basic and Primary, with varying prices across four cabin categories: interior, oceanview, balcony, and suite. Basic cabins are not available for the suite category. The price per night for each cabin type and category is as follows: Cabin Type Cabin Category Interior Oceanview Balcony Suite Basic $$85$ $$100$ $$115$ N$/$A Primary $$100$ $$120$ $$145$ $$180$ The cruise line uses a demand forecasting system to predict cabin bookings for future voyages and aims to maximize revenue by determining the optimal number of reservations to accept for each cabin type and category. The demand forecast for an upcoming voyage estimates the following demands: $100$ interior cabins, $140$ oceanview cabins, $120$ balcony cabins, and $70$ suite cabins. The cruise ship has a total of $180$ Basic cabins and $220$ Primary cabins. The manager observes that the ship cannot accommodate all of the expected demand $($Data see Q$1$ in Data File$).1)$ Formulate the problem as a linear programming. Clear define the decision variable$($s$),$ objective function, and constraints by presenting the conceptual model $($see the instruction above in red$).$ Requirement: for the conceptual model, the objective function and constraints should clearly demonstrate mathematical relationships. $2)$ Develop an Excel model to determine how the ship$$s manager should allocate the cabins, and provide your answer. Which cabin category demands cannot be fully satisfied? $3)$ With some effort, an unused crew area could be converted into a cabin. If the conversion cost is the same for both types of cabins, clearly provide a solution map indicating any additional constraint$($s$)$ that should be included or changes to the constraint$($s$)$ in Question $1)$ to recommend whether the cruise line should convert the space into a Basic or Primary cabin.