Reference no: EM132701589

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 0.2×a^1/2 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% (= 0.2×4^1/2) of other brands' customers switch to Huggys. J&J wants to maximize its average market share during the next 12 months.

1. Define the decision variables and write down the detailed mathematical formulation of J&J's optimization problem.
2. Solve the optimization problem by Excel Solver. Write down J&J's detailed optimal advertising plan during the next 12 months and optimal average market share.