Procter & Gamble $($P&G$)$ produces hundreds of products across multiple product categories. Its many billion$-$dollar brands$-$like Bounty paper towels and Crest toothpaste$-$are well known in the industry and by millions of consumers around the world.$*$ P&G$\text{'}$s marketing departments have millions of dollars at their disposal to market P&G products across different channels, to reach consumers where they live, work, and shop.

Assume that you are one of the marketing managers for P&G$\text{'}$s Hair Care category, including products such as Head & Shoulders and Pantene. You and your team have been tasked with allocating $$20$ million to different distribution channels to connect P&G$\text{'}$s Hair Care brands with consumers. Which distribution channels are available to you, and which would prove most effective?