1. (a) What is a linear optimization problem with multiple optimal solutions? How do we find if a given linear optimization problem has multiple optimal solutions? Give a real-world example of a linear optimization problem where multiple optimal solutions may occur.

(b) Explain how the simulation process is used in business analytics models. What are the advantages of using simulation? What are its limitations? How can a simulation model be verified? Give a real-world example where using simulation is appropriate. Use at least 10 sentences to answer this question.

(c) What is a marketing problem in applications of linear optimization? Briefly discuss the decision variables, the objective function, and the constraint requirements in a marketing problem. Give a real-world example of a marketing problem. Answer in at least eight sentences.

(d) Describe the concept and process of spreadsheet modeling and analysis. Give a real-world example where spreadsheet modeling and analysis are useful. Answer in at least eight sentences.