Question 68
In each cell of a $2025 \times 2025$ board, a nonnegative real number is written in such a way that the sum of the numbers in each row is equal to $1$, and the sum of the numbers in each column is equal to $1$. Define $r_{i}$ to be the largest value in row $i$, and let $R = r_{1} + r_{2} + \dots + r_{2025}$. Similarly, define $c_{i}$ to be the largest value in column $i$, and let $C = c_{1} + c_{2} + \dots + c_{2025}$. What is the largest possible value of $\frac{R}{C}$?