Proctor and Ramble 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...

Proctor and Ramble 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 Proctor and Ramble’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. (Hint: Make sure you enter a nonzero trial value for each month’s advertising expense or Solver might give you an error message.)