Final answer:
The Borda count method assigns points to candidates based on their ranking on each voter's ballot, and the maximum number of points a candidate can earn in this method is 465 points.
Step-by-step explanation:
The Borda count method assigns points to candidates based on their ranking on each voter's ballot. In this method, the candidate ranked first receives the highest number of points, the candidate ranked second receives a slightly lower number of points, and so on.
If there are three candidates and 30 voters, the maximum number of points a candidate can earn is calculated by summing up the points for each ranking position for all voters. In this case, the maximum number of points is 30 + 29 + 28 + ... + 1, which can be found using the formula for the sum of an arithmetic series:
Maximum points = (n/2)(first term + last term),
where n is the number of terms in the series. Therefore, the maximum number of points a candidate can earn is:
Maximum points = (30/2)(1 + 30) = 15 x 31 = 465 points.