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 0.2a12 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. (Hint:

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