How about if we had a budget of $20 million instead of $10 million? (c) Now, let us build an optimization model to select hotels. We are trying to decide whether or not a hotel should be purchased, while making sure we spend no more than our budget of $10 million. Our objective is to maximize the total predicted Profitability. (i) Write out the optimization problem we are trying to solve. Make sure to describe the decision variables, the objective, and the constraints. (ii) Now solve your optimization model. What is the optimal solution? Report the values of the decision variables and the optimal objective function value. (iii) Does the optimal solution make sense intuitively? How does it compare to the greedy solution? (d) La Quinta thinks that buying too many hotels in one city is probably not a good idea, and would prefer to diversify across as many cities as possible. Add constraint(s) to your model to limit the number of hotels purchased in any city to at most 2. (i) What are the constraints that you need to add to the model? Intuitively, do you expect the new optimal objective function value to be larger, smaller, or the same as before? (ii) Solve the new model. What is the optimal solution? Give the values of the decision variables and the optimal objective function value. How does this compare to the previous solution? (e) In no more than one paragraph, describe how you would present your results to La Quinta. Do you have any recommendations for them to improve the regression model? How about to improve the optimization model? How about if we had a budget of $20 million instead of $10 million? (c) Now, let us build an optimization model to select hotels. We are trying to decide whether or not a hotel should be purchased, while making sure we spend no more than our budget of $10 million. Our objective is to maximize the total predicted Profitability. (i) Write out the optimization problem we are trying to solve. Make sure to describe the decision variables, the objective, and the constraints. (ii) Now solve your optimization model. What is the optimal solution? Report the values of the decision variables and the optimal objective function value. (iii) Does the optimal solution make sense intuitively? How does it compare to the greedy solution? (d) La Quinta thinks that buying too many hotels in one city is probably not a good idea, and would prefer to diversify across as many cities as possible. Add constraint(s) to your model to limit the number of hotels purchased in any city to at most 2. (i) What are the constraints that you need to add to the model? Intuitively, do you expect the new optimal objective function value to be larger, smaller, or the same as before? (ii) Solve the new model. What is the optimal solution? Give the values of the decision variables and the optimal objective function value. How does this compare to the previous solution? (e) In no more than one paragraph, describe how you would present your results to La Quinta. Do you have any recommendations for them to improve the regression model? How about to improve the optimization model
