Problem 2 [30 points): J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. At the beginning of January, Huggys has a 30% market share. During any month, 10% of the people who purchase Huggys switch to other brands, and a fraction 0.2xa1/2 of customers who usually buy other brands switch to Huggys, where a is the amount spent on advertising in millions of dollars. For example, if you spend $4 million during a month, 40% of other brands' customers switch to Huggys. J&J wants to maximize its average market share during the next 12 months. 1 a) Define the decision variables and write down the detailed mathematical formulation of J&J's optimization problem. [15 points] b) Solve the optimization problem by Excel Solver. [10 points] c) What are J&J's optimal advertising plan and average market share? [5 points] Problem 2 [30 points): J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. At the beginning of January, Huggys has a 30% market share. During any month, 10% of the people who purchase Huggys switch to other brands, and a fraction 0.2xa1/2 of customers who usually buy other brands switch to Huggys, where a is the amount spent on advertising in millions of dollars. For example, if you spend $4 million during a month, 40% of other brands' customers switch to Huggys. J&J wants to maximize its average market share during the next 12 months. 1 a) Define the decision variables and write down the detailed mathematical formulation of J&J's optimization problem. [15 points] b) Solve the optimization problem by Excel Solver. [10 points] c) What are J&J's optimal advertising plan and average market share? [5 points]