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 defect to brand X, and a fraction 0.2a^1/2 of customers who usually buy brand X 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 brand X’s customers switch to Huggys. Your goal is to maximize J&J’s average market share during the next 12 months, where the average is computed from each month’s ending share. Determine an appropriate advertising policy.