Final answer:
Dynamic programming can be applied to optimize the distribution of TV commercials across different broadcasting areas to maximize votes in an election. It involves creating a table to calculate the maximum votes for each allocation of commercials and choosing the best option based on potential gains from each area.
Step-by-step explanation:
To maximize the estimated number of additional votes, we can use dynamic programming, a method for solving complex problems by breaking them down into simpler subproblems. The problem is essentially an optimization problem where we have a limited number of resources (five commercials) that need to be allocated across multiple choices (four broadcasting areas) to achieve the maximum outcome (votes).
We begin by constructing a table where the rows represent the number of commercials available and the columns represent the four areas. Our goal is to populate this table with the maximum votes that can be attained with a certain number of commercials in each area. By evaluating the table entries, we can gradually build up the solution for the entire problem.
The challenge is to decide where to place each commercial, based on the potential gains. When assigning a commercial to an area, we must consider the additional votes it would provide compared to placing it in another area. The optimal distribution of commercials is found by choosing the best option at each step, taking into account the remaining commercials and the possible additional votes for each area.
The specifics of the dynamic programming algorithm would require a series of steps to fill in the table and then trace back the decisions made, to determine the optimal distribution. Unfortunately, the question does not provide enough data to complete the entire table, but this explanation outlines the methodological approach to solving the problem.